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Preface 9 Preface to second edition 9 Preface to first edition 9 Overview 11 For the Reader 12 For the Instructor 13 For the Expert 13 Acknowledgements 16 Part I: Basic Methods and Examples 17 Chapter 1. Introduction to Finite Markov Chains 18 1.1. Markov Chains 18 1.2. Random Mapping Representation 21 1.3. Irreducibility and Aperiodicity 23 1.4. Random Walks on Graphs 24 1.5. Stationary Distributions 25 1.6. Reversibility and Time Reversals 29 1.7. Classifying the States of a Markov Chain* 31 Exercises 33 Notes 34 Chapter 2. Classical (and Useful) Markov Chains 37 2.1. Gambler's Ruin 37 2.2. Coupon Collecting 38 2.3. The Hypercube and the Ehrenfest Urn Model 39 2.4. The Pólya Urn Model 41 2.5. Birth-and-Death Chains 42 2.6. Random Walks on Groups 43 2.7. Random Walks on Z and Reflection Principles 46 Exercises 50 Notes 51 Chapter 3. Markov Chain Monte Carlo: Metropolis and Glauber Chains 54 3.1. Introduction 54 3.2. Metropolis Chains 54 3.3. Glauber Dynamics 57 Exercises 61 Notes 61 Chapter 4. Introduction to Markov Chain Mixing 63 4.1. Total Variation Distance 63 4.2. Coupling and Total Variation Distance 65 4.3. The Convergence Theorem 68 4.4. Standardizing Distance from Stationarity 69 4.5. Mixing Time 70 4.6. Mixing and Time Reversal 71 4.7. p Distance and Mixing 72 Exercises 73 Notes 74 Chapter 5. Coupling 76 5.1. Definition 76 5.2. Bounding Total Variation Distance 78 5.3. Examples 78 5.4. Grand Couplings 85 Exercises 89 Notes 90 Chapter 6. Strong Stationary Times 91 6.1. Top-to-Random Shuffle 91 6.2. Markov Chains with Filtrations 92 6.3. Stationary Times 93 6.4. Strong Stationary Times and Bounding Distance 94 6.5. Examples 97 6.6. Stationary Times and Cesaro Mixing Time 100 6.7. Optimal Strong Stationary Times* 101 Exercises 102 Notes 103 Chapter 7. Lower Bounds on Mixing Times 104 7.1. Counting and Diameter Bounds 104 7.2. Bottleneck Ratio 105 7.3. Distinguishing Statistics 108 7.4. Examples 112 Exercises 114 Notes 115 Chapter 8. The Symmetric Group and Shuffling Cards 116 8.1. The Symmetric Group 116 8.2. Random Transpositions 118 8.3. Riffle Shuffles 123 Exercises 126 Notes 128 Chapter 9. Random Walks on Networks 132 9.1. Networks and Reversible Markov Chains 132 9.2. Harmonic Functions 133 9.3. Voltages and Current Flows 134 9.4. Effective Resistance 135 9.5. Escape Probabilities on a Square 140 Exercises 141 Notes 143 Chapter 10. Hitting Times 144 10.1. Definition 144 10.2. Random Target Times 145 10.3. Commute Time 147 10.4. Hitting Times on Trees 150 10.5. Hitting Times for Eulerian Graphs 153 10.6. Hitting Times for the Torus 153 10.7. Bounding Mixing Times via Hitting Times 156 10.8. Mixing for the Walk on Two Glued Graphs 160 Exercises 162 Notes 165 Chapter 11. Cover Times 166 11.1. Definitions 166 11.2. The Matthews Method 166 11.3. Applications of the Matthews Method 168 11.4. Spanning Tree Bound for Cover Time 170 11.5. Waiting for all patterns in coin tossing 172 Exercises 174 Notes 174 Chapter 12. Eigenvalues 177 12.1. The Spectral Representation of a Reversible Transition Matrix 177 12.2. The Relaxation Time 179 12.3. Eigenvalues and Eigenfunctions of Some Simple Random Walks 181 12.4. Product Chains 185 12.5. Spectral Formula for the Target Time 188 12.6. An 2 Bound 188 12.7. Time Averages 189 Exercises 193 Notes 194 Part II: The Plot Thickens 195 Chapter 13. Eigenfunctions and Comparison of Chains 196 13.1. Bounds on Spectral Gap via Contractions 196 13.2. The Dirichlet Form and the Bottleneck Ratio 197 13.3. Simple Comparison of Markov Chains 201 13.4. The Path Method 203 13.5. Wilson's Method for Lower Bounds 208 13.6. Expander Graphs* 212 Exercises 214 Notes 215 Chapter 14. The Transportation Metric and Path Coupling 217 14.1. The Transportation Metric 217 14.2. Path Coupling 219 14.3. Rapid Mixing for Colorings 222 14.4. Approximate Counting 225 Exercises 228 Notes 230 Chapter 15. The Ising Model 231 15.1. Fast Mixing at High Temperature 231 15.2. The Complete Graph 234 15.3. The Cycle 235 15.4. The Tree 236 15.5. Block Dynamics 239 15.6. Lower Bound for Ising on Square* 242 Exercises 244 Notes 245 Chapter 16. From Shuffling Cards to Shuffling Genes 248 16.1. Random Adjacent Transpositions 248 16.2. Shuffling Genes 252 Exercise 257 Notes 257 Chapter 17. Martingales and Evolving Sets 259 17.1. Definition and Examples 259 17.2. Optional Stopping Theorem 260 17.3. Applications 262 17.4. Evolving Sets 265 17.5. A General Bound on Return Probabilities 269 17.6. Harmonic Functions and the Doob h-Transform 271 17.7. Strong Stationary Times from Evolving Sets 272 Exercises 275 Notes 275 Chapter 18. The Cutoff Phenomenon 277 18.1. Definition 277 18.2. Examples of Cutoff 278 18.3. A Necessary Condition for Cutoff 283 18.4. Separation Cutoff 284 Exercises 285 Notes 285 Chapter 19. Lamplighter Walks 288 19.1. Introduction 288 19.2. Relaxation Time Bounds 289 19.3. Mixing Time Bounds 291 19.4. Examples 293 Exercises 293 Notes 294 Chapter 20. Continuous-Time Chains* 296 20.1. Definitions 296 20.2. Continuous-Time Mixing 297 20.3. Spectral Gap 300 20.4. Product Chains 301 Exercises 305 Notes 306 Chapter 21. Countable State Space Chains* 307 21.1. Recurrence and Transience 307 21.2. Infinite Networks 309 21.3. Positive Recurrence and Convergence 311 21.4. Null Recurrence and Convergence 316 21.5. Bounds on Return Probabilities 317 Exercises 318 Notes 320 Chapter 22. Monotone Chains 321 22.1. Introduction 321 22.2. Stochastic Domination 322 22.3. Definition and Examples of Monotone Markov Chains 324 22.4. Positive Correlations 325 22.5. The Second Eigenfunction 329 22.6. Censoring Inequality 330 22.7. Lower bound on 335 22.8. Proof of Strassen's Theorem 336 22.9. Exercises 337 22.10. Notes 338 Chapter 23. The Exclusion Process 339 23.1. Introduction 339 23.2. Mixing Time of k-exclusion on the n-path 344 23.3. Biased Exclusion 345 23.4. Exercises 349 23.5. Notes 350 Chapter 24. Cesàro Mixing Time, Stationary Times, and Hitting Large Sets 351 24.1. Introduction 351 24.2. Equivalence of tstop, tCes and tG for reversible chains 353 24.3. Halting States and Mean-Optimal Stopping Times 355 24.4. Regularity Properties of Geometric Mixing Times 356 24.5. Equivalence of tG and tH 357 24.6. Upward Skip-Free Chains 358 24.7. tH() are comparable for 1/2. 359 24.8. An Upper Bound on trel 360 24.9. Application to Robustness of Mixing 361 Exercises 362 Notes 362 Chapter 25. Coupling from the Past 364 25.1. Introduction 364 25.2. Monotone CFTP 365 25.3. Perfect Sampling via Coupling from the Past 370 25.4. The Hardcore Model 371 25.5. Random State of an Unknown Markov Chain 373 Exercise 374 Notes 374 Chapter 26. Open Problems 375 26.1. The Ising Model 375 26.2. Cutoff 376 26.3. Other Problems 376 26.4. Update: Previously Open Problems 377 Appendix A. Background Material 379 A.1. Probability Spaces and Random Variables 379 A.2. Conditional Expectation 385 A.3. Strong Markov Property 388 A.4. Metric Spaces 389 A.5. Linear Algebra 390 A.6. Miscellaneous 390 Exercises 390 Appendix B. Introduction to Simulation 391 B.1. What Is Simulation? 391 B.2. Von Neumann Unbiasing* 392 B.3. Simulating Discrete Distributions and Sampling 393 B.4. Inverse Distribution Function Method 394 B.5. Acceptance-Rejection Sampling 394 B.6. Simulating Normal Random Variables 396 B.7. Sampling from the Simplex 398 B.8. About Random Numbers 398 B.9. Sampling from Large Sets* 399 Exercises 402 Notes 405 Appendix C. Ergodic Theorem 406 C.1. Ergodic Theorem* 406 Exercise 407 Appendix D. Solutions to Selected Exercises 408 Bibliography 438 Notation Index 453 Index 455

本书是对Markov链理论的现代处理方法的导引,该方法的主要目标是确定一个Markov链收敛到作为态空间体积和几何之函数的平稳分布的收敛速率。作者发展了估计收敛时间的关键工具,包括耦合、强平稳时间以及谱方法:一有可能,便强调概率论式的方法。本书包括了许多例题并对统计力学的中心模型给出了简短介绍;还讲述了网络上的随机游动,包括击中和掩盖时间,以及对洗牌的各种方法的分析。至于预备知识,作者假定了对概率论的适度了解以及大学水平的线性代数。本书打算将这个活跃的研究领域的激情带给大范围的受众。

<p><p>the Book Examines In Some Depth Two Important Classes Of Point Processes, Determinantal Processes And ''gaussian Zeros'', I.e., Zeros Of Random Analytic Functions With Gaussian Coefficients. These Processes Share A Property Of ''point-repulsion'', Where Distinct Points Are Less Likely To Fall Close To Each Other Than In Processes, Such As The Poisson Process, That Arise From Independent Sampling. Nevertheless, The Treatment In The Book Emphasizes The Use Of Independence&#58; For Random Power Series, The Independence Of Coefficients Is Key; For Determinantal Processes, The Number Of Points In A Domain Is A Sum Of Independent Indicators, And This Yields A Satisfying Explanation Of The Central Limit Theorem (clt) For This Point Count. Another Unifying Theme Of The Book Is Invariance Of Considered Point Processes Under Natural Transformation Groups. The Book Strives For Balance Between General Theory And Concrete Examples. On The One Hand, It Presents A Primer On Modern Techniques On The Interface Of Probability And Analysis. On The Other Hand, A Wealth Of Determinantal Processes Of Intrinsic Interest Are Analyzed; These Arise From Random Spanning Trees And Eigenvalues Of Random Matrices, As Well As From Special Power Series With Determinantal Zeros. The Material In The Book Formed The Basis Of A Graduate Course Given At The Ias-park City Summer School In 2007; The Only Background Knowledge Assumed Can Be Acquired In First-year Graduate Courses In Analysis And Probability.<br></p>

Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and connections on random walks on graphs to embedding in Hilbert space. This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike.

<p><P>This book is an introduction to the modern approach to the theory of Markov chains. The main goal of this approach is to determine the rate of convergence of a Markov chain to the stationary distribution as a function of the size and geometry of the state space. The authors develop the key tools for estimating convergence times, including coupling, strong stationary times, and spectral methods. Whenever possible, probabilistic methods are emphasized. The book includes many examples and provides brief introductions to some central models of statistical mechanics. Also provided are accounts of random walks on networks, including hitting and cover times, and analyses of several methods of shuffling cards. As a prerequisite, the authors assume a modest understanding of probability theory and linear algebra at an undergraduate level. Markov Chains and Mixing Times is meant to bring the excitement of this active area of research to a wide audience.</p>

Предлагаемая читателю книга американских математиков Самюэля Карлина и Вильяма Стаддена необычайно привлекательна богатством приложений излагаемой в ней фундаментальной теории. Приложения в области анализа, теории вероятностей, математической статистики и теории планирования эксперимента делают эту книгу весьма актуальной.

Титульный лист ......Page 1 Выходные данные ......Page 2 ОГЛАВЛЕНИЕ ......Page 3 Предисловие редактора ......Page 7 Предисловие авторов к американскому изданию ......Page 9 Список основных обозначений ......Page 12 § 1. Системы Чебышева ......Page 13 § 2. Обобщенные и слабые системы Чебышева ......Page 15 § 3. Примеры ......Page 20 § 4. Эквивалентное определение $T$-систем для многочленов ......Page 31 § 5. Многочлены с заданными нулями ......Page 38 § 6. Задача интерполяции ......Page 41 Глава II. Моментные пространства, индуцированные $T$-системами, и двойственные к ним ......Page 48 § 1. Определение и общая структура $\mathcal{M}_{n+1}$ ......Page 49 § 2. Граница и крайние лучи $\mathcal{M}_{n+1}$ ......Page 52 § 3. Внутренность $\mathcal{M}_{n+1}$ ......Page 55 § 4. Экстремальная характеризация канонической меры ......Page 59 § 5. Свойства непрерывности канонического представления ......Page 61 § 6. Иной подход к каноническим мерам и одномерным сечениям ......Page 64 § 7. Двумерные сечения ......Page 66 § 8. Монотонность корней некоторых главных представлений ......Page 69 § 9. Двойственный конус $\mathcal{P}_{n+1}$ ......Page 73 § 10. Теоремы о представлении положительных многочленов ......Page 75 § 11. Крайние точки $\mathcal{P}_{n+1}$ ......Page 85 Глава III. Теорема Маркова — Крейна и ее ответвления ......Page 87 § 1. Экстремальные значения из $R(с^0)$ ......Page 88 § 2. Теорема Маркова—Крейна ......Page 89 § 3. Другое доказательство теоремы Маркова—Крейна ......Page 91 § 4. Обобщения ......Page 97 § 5. Множества мер, заданных моментными неравенствами ......Page 103 § 6. Крайние точки множества функций распределения с заданными моментами ......Page 108 § 1. Классический критерий для моментных точек ......Page 113 § 2. Опорные гиперплоскости и ортогональные многочлены ......Page 115 § 3. Максимальная масса $\rho(t_0)$ ......Page 121 § 4. Геометрия классических чебышевских многочленов ......Page 125 § 5. Симплексы $S_n$ и $B_n$ ......Page 130 § 6. Объем симплекса ......Page 134 § 7. Свойства симметрии моментных пространств ......Page 137 § 8. Механические квадратуры и главные представления ......Page 143 § 9. Сплайн-функции с заданными нулями ......Page 147 § 2. Общая теорема о конической оболочке ......Page 152 § 3. Общая структура $\mathcal{M}_{n+1}$ ......Page 154 § 4. Канонические представления, максимальная масса $\rho(t_0)$ и двумерные сечения ......Page 160 § 5. Теорема Маркова—Крейна ......Page 164 § 6. Другой класс экстремальных задач, решениями которых являются канонические меры ......Page 167 § 7. Применения теории канонических мер и аппроксимации преобразований Лапласа—Стилтьеса ......Page 170 § 8. Теоремы о представлении положительных многочленов ......Page 175 § 9. Крайние точки и граница $\mathcal{P}_{n+1}[0,\infty)$ ......Page 178 § 10. Классический критерий для моментных точек ......Page 179 § 11. Соотношение между $\mathcal{P}_{n+1}$ и $\mathcal{M}_{n+1}$ ......Page 180 § 12. Соотношение между $\mathcal{M}^n[0,a]$ и $\mathcal{M}^n[0,\infty)$ ......Page 184 § 1. Определения ......Page 186 § 2. Основные свойства периодических $T$-систем ......Page 187 § 3. Двумерные сечения ......Page 188 § 4. Тригонометрическая проблема моментов ......Page 191 § 5. Примеры ......Page 192 § 6. Представление для положительных многочленов и крайние точки $\mathcal{M}_{2m+1}$ ......Page 197 § 7. Чебышевские системы на $(—\infty,\infty)$ ......Page 201 § 8. Представления для многочленов в $\mathcal{P}_{2m+1}(—\infty,\infty)$ ......Page 203 § 9. Двумерные сечения для ${t^i}_0^{2m}$ на $(—\infty,\infty)$ ......Page 204 § 10. Двумерные сечения для ${t^i}_0^{2m+1}$ на $(—\infty,\infty)$ ......Page 206 § 11. Соотношение между $\mathcal{P}_{n+1}$ и $\mathcal{M}_{n+1}$ ......Page 208 § 1. Введение ......Page 209 § 2. Индекс множества $\Sigma<К$ ......Page 212 § 3. Многочлены с заданными нулями ......Page 214 § 4. Граница и канонические представления точек в $\mathcal{M}_{n+1}(\bar{K})$ ......Page 216 § 5. Главные представления ......Page 219 § 6. Свойства перемежаемости корней канонических представлений ......Page 222 § 7. Теорема Маркова—Крейна ......Page 224 § 8. Дополнения ......Page 227 § 9. Другой класс экстремальных задач, решениями которых являются канонические меры ......Page 228 § 10. Применения к теории интерполяции абсолютно монотонных функций ......Page 232 § 1. Введение ......Page 236 § 2. Граница и общие свойства моментного пространства $\Phi_{n+1}$ ......Page 237 § 3. Главные представления внутренних точек ......Page 241 § 4. Другой подход к построению главных представлений ......Page 243 § 5. Пополнение чебышевской системы, определенной на открытом интервале ......Page 244 § 6. Свойства перемежаемости узлов канонических представлений ......Page 249 § 7. Двумерные сечения ......Page 253 § 8. Неравенства чебышевского типа ......Page 254 § 9. Множества мер, определяемых моментными неравенствами ......Page 257 § 10. Обобщения ......Page 261 § 11. Задача минимизации ......Page 262 § 12. Теорема Ляпунова о множестве значений векторной меры ......Page 267 § 13. Обобщения теоремы Ляпунова ......Page 272 § 14. Применения теоремы Ляпунова ......Page 276 Глава IX. Минимаксная аппроксимация, неравенство Маркова—Бернштейна и связанные с ними задачи ......Page 281 § 1. Многочлены наилучшего приближения ......Page 282 § 2. Многочлены наилучшего приближения (продолжение) ......Page 285 § 3. Доказательство теоремы 1.1 ......Page 287 § 4. Примеры применения теоремы 1.1 ......Page 289 § 5. Обобщение неравенства Маркова—Бернштейна ......Page 294 § 6. Обобщение неравенства Маркова—Бернштейна для бесконечных интервалов ......Page 299 § 7. Обобщенные неравенства Маркова—Бернштейна для периодических функций ......Page 301 § 8. Примеры и приложения ......Page 305 § 9. Дополнения ......Page 311 § 10. Периодические $ET$-системы и экстремальные задачи с двумя ограничениями ......Page 316 § 1. Введение ......Page 319 § 2. Общая теорема эквивалентности ......Page 321 § 3. Максимизация некоторых определителей ......Page 327 § 4. Обобщение задачи Фейера ......Page 333 § 5. Устойчивые и экономичные интерполяционные системы ......Page 336 § 6. Тригонометрические системы ......Page 341 § 7. Планы эксперимента ......Page 348 § 8. Обобщения ......Page 362 § 9. Открытые вопросы ......Page 372 § 1. Предварительные замечания ......Page 374 § 2. Свойства конуса $C(u_0,u_1,\ldots,u_n)$ ......Page 379 § 3. Дальнейшие свойства конуса $C(u_0,u_1,\ldots,u_n)$ ......Page 391 § 4. Крайние лучи конусов ......Page 394 § 5. Конус, дуальный к конусу $C(u_0,\ldots,u_n)$ ......Page 402 § 6. Примеры и приложения теории дуальных конусов ......Page 408 § 7. Дискретные примеры ......Page 418 § 8. Обобщенные абсолютно монотонные функции ......Page 430 § 9. Интерполяция функций обобщенными сплайн-многочленами ......Page 435 § 10. Наилучшие квадратурные формулы, использующие натуральные сплайн-многочлены ......Page 444 § 11. Свойства дифференцируемости выпуклых в обобщенном смысле функций ......Page 452 § 1. Введение ......Page 464 § 2. Общая теорема ......Page 467 § 3. Примеры ......Page 471 § 4. Чебышевские неравенства для классов унимодальных распределений ......Page 478 § 5. Унимодальность высшего порядка ......Page 490 § 1. Введение ......Page 497 § 2. Крайние точки множества $\mathcal{A}$ ......Page 500 § 3. Чебышевские неравенства для Pr$(\max\limits_{1\leq i\leq n} |Х_i| \geq 1)$ ......Page 504 § 4. Обобщения неравенства Берге ......Page 509 § 5. Чебышевские неравенства, в которых $\Omega(\vec{x})$ — симметрическая характеристическая функция ......Page 510 § 6. Чебышевские неравенства для прямоугольника ......Page 514 § 7. Неравенства для Pr$(\max\limits_{1\leq i\leq n} Х_i \geq 1)$ ......Page 516 § 8. Чебышевские неравенства для случая, когда $\Omega$ есть характеристическая функция конечного объединения выпуклых областей ......Page 517 § 9. Границы для минимальных компонент ......Page 521 § 1. Формулировка теорем ......Page 523 § 2. Доказательство теорем 1.1—1.4 ......Page 527 § 3. Гипотеза Самуэльса ......Page 531 § 4. Неравенство для сумм случайных величин без предположения независимости ......Page 536 § 5. Нелинейные задачи ......Page 539 § 6. Пример I. Максимум и размах выборки ......Page 541 § 7. Пример II. ......Page 550 Библиография ......Page 554 Литература, добавленная при переводе ......Page 564 Предметный указатель ......Page 566

Lonely Planet: The world's leading travel guide publisher Lonely Planet Canada is your passport to the most relevant, up-to-date advice on what to see and skip, and what hidden discoveries await you. Hike the Rockies, marvel at the Northern Lights, or indulge in cultural delights from Montreal's cafe culture to the island villages of Haida Gwaii; all with your trusted travel companion. Get to the heart of Canada and begin your journey now! Lonely Planet Canada Travel Guide: Color maps and images throughout Highlights and itineraries help you tailor your trip to your personal needs and interests Insider tips to save time and money and get around like a local, avoiding crowds and trouble spots Essential info at your fingertips - hours of operation, phone numbers, websites, transit tips, prices Honest reviews for all budgets - eating, sleeping, sight-seeing, going out, shopping, hidden gems that most guidebooks miss Cultural insights give you a richer, more rewarding travel experience - history, Aboriginal cultures, outdoor activities, wildlife, wine, cuisine, epic drives, national parks Free, convenient pull-out Vancouver map (included in print version), plus over 100 maps Covers Vancouver, Toronto, Montreal, Quebec City, British Columbia, the Rocky Mountains, Nova Scotia, Prince Edward Island, Alberta, Newfoundland, Banff, New Brunswick, Yukon Territory and more. About Lonely Planet: Since 1973, Lonely Planet has become the world's leading travel media company with guidebooks to every destination, an award-winning website, mobile and digital travel products, and a dedicated traveller community. Lonely Planet covers must-see spots but also enables curious travellers to get off beaten paths to understand more of the culture of the places in which they find themselves. The world awaits! Lonely Planet guides have won the TripAdvisor Traveler's Choice Award in 2012, 2013, 2014, 2015, and 2016. 'Lonely Planet. It's on everyone's bookshelves; it's in every traveller's hands. It's on mobile phones. It's on the Internet. It's everywhere, and it's telling entire generations of people how to travel the world.' -- Fairfax Media 'Lonely Planet guides are, quite simply, like no other.' - New York Times Important Notice: The digital edition of this book may not contain all of the images found in the physical edition.

<p><P>This book is an introduction to the modern approach to the theory of Markov chains. The main goal of this approach is to determine the rate of convergence of a Markov chain to the stationary distribution as a function of the size and geometry of the state space. The authors develop the key tools for estimating convergence times, including coupling, strong stationary times, and spectral methods. Whenever possible, probabilistic methods are emphasized. The book includes many examples and provides brief introductions to some central models of statistical mechanics. Also provided are accounts of random walks on networks, including hitting and cover times, and analyses of several methods of shuffling cards. As a prerequisite, the authors assume a modest understanding of probability theory and linear algebra at an undergraduate level. Markov Chains and Mixing Times is meant to bring the excitement of this active area of research to a wide audience.</p>

<p><p>the Book Examines In Some Depth Two Important Classes Of Point Processes, Determinantal Processes And ''gaussian Zeros'', I.e., Zeros Of Random Analytic Functions With Gaussian Coefficients. These Processes Share A Property Of ''point-repulsion'', Where Distinct Points Are Less Likely To Fall Close To Each Other Than In Processes, Such As The Poisson Process, That Arise From Independent Sampling. Nevertheless, The Treatment In The Book Emphasizes The Use Of Independence&#58; For Random Power Series, The Independence Of Coefficients Is Key; For Determinantal Processes, The Number Of Points In A Domain Is A Sum Of Independent Indicators, And This Yields A Satisfying Explanation Of The Central Limit Theorem (clt) For This Point Count. Another Unifying Theme Of The Book Is Invariance Of Considered Point Processes Under Natural Transformation Groups. The Book Strives For Balance Between General Theory And Concrete Examples. On The One Hand, It Presents A Primer On Modern Techniques On The Interface Of Probability And Analysis. On The Other Hand, A Wealth Of Determinantal Processes Of Intrinsic Interest Are Analyzed; These Arise From Random Spanning Trees And Eigenvalues Of Random Matrices, As Well As From Special Power Series With Determinantal Zeros. The Material In The Book Formed The Basis Of A Graduate Course Given At The Ias-park City Summer School In 2007; The Only Background Knowledge Assumed Can Be Acquired In First-year Graduate Courses In Analysis And Probability.<br></p>

<p>'This is a powerfully beautiful country, captivating to the eyes and soul, and as such, the subject of many Jamaican poems, songs and deep wells of nostalgia.' – Adam Karlin, Lonely Planet Writer</p><p class=null1>Our Promise</p><p>You can trust our travel information because Lonely Planet authors visit the places we write about, each and every edition. We never accept freebies for positive coverage, and you can rely on us to tell it like we see it.</p><p class=null1>Inside This Book…</p><p>2 authors<br>52 days of research<br>63 bottles of Red Stripe Miles of Caribbean coastline Inspirational photos Easy-to-use maps In-depth background At-a-glance practical info Outdoor activities chapter Comprehensive planning tools</p>

М.: Международные отношения, 1967. — 210 стр. Выберите нужное слово. Учебное пособие. Очень полезная книга для всех изучающих немецкий язык. Рассматриваются трудности, связанные с отсутствием привычки у русского дифференцировать значения, которые выражены в русском языке унифицировано. Типичные лексические ошибки, которые обычно делают русские заключаются в неправильном выборе немецкого эквивалента (например, в употреблении слова „verzichten вместо „aufgeben) или в том, что немецкому слову приписывается более широкая семантика их русского эквивалента. (Например, „Er beschloß, daß er sehr klug ist" вместо „Er dachte (glaubte), daß er sehr klug ist".) В книге дается объяснение употребления немецких эквивалентов в двух планах: в плане сопоставления с русским языком и в плане выявления оттенков значения и специфики употребления внутри самого немецкого языка. Имеется обширный набор упражнений для закрепления различного уровня сложности. Качество файла - OCR, распознан на 90%, возможны ошибки.

« Les affaires privées se règlent en privé », affirmait-il. François Hollande l’avait promis, il serait un président « exemplaire ». Il est devenu le héros d’un vaudeville dont s’est gaussée la France entière. Une affaire de cœur, de casque intégral et de dérobades à scooter. Était-ce écrit ? Était-il inscrit quelque part, loin des incertitudes du hasard, que les élans de ce chef d’État marqueraient à ce point son quinquennat ? Valérie, Ségolène, Julie, c’est sa vie. Mais c’est aussi la nôtre, notre vie publique, qui, depuis deux ans, s’en trouve parasitée. Jamais la confusion des genres n’avait été portée à cette extrémité.

Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and connections on random walks on graphs to embedding in Hilbert space. This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike.

Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and connections on random walks on graphs to embedding in Hilbert space. This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike.

“This is a powerfully beautiful country, captivating to the eyes and soul, and as such, the subject of many Jamaican poems, songs and deep wells of nostalgia.” – Adam Karlin, Lonely Planet Writer Our Promise You can trust our travel information because Lonely Planet authors visit the places we write about, each and every edition. We never accept freebies for positive coverage, and you can rely on us to tell it like we see it. Inside This Book... 2 authors 52 days of research 63 bottles of Red Stripe Miles of Caribbean coastline Inspirational photos Easy-to-use maps In-depth background At-a-glance practical info Outdoor activities chapter Comprehensive planning tools<BR>

Part I, Bertoin, J.: Subordinators: Examples and Applications: Foreword.- Elements on subordinators.- Regenerative property.- Asymptotic behaviour of last passage times.- Rates of growth of local time.- Geometric properties of regenerative sets.- Burgers equation with Brownian initial velocity.- Random covering.- Lévy processes.- Occupation times of a linear Brownian motion.- Part II, Martinelli, F.: Lectures on Glauber Dynamics for Discrete Spin Models: Introduction.- Gibbs Measures of Lattice Spin Models.- The Glauber Dynamics.- One Phase Region.- Boundary Phase Transitions.- Phase Coexistence.- Glauber Dynamics for the Dilute Ising Model.- Part III, Peres, Yu.: Probability on Trees: An Introductory Climb: Preface.- Basic Definitions and a Few Highlights.- Galton-Watson Trees.- General percolation on a connected graph.- The first-Moment method.- Quasi-independent Percolation.- The second Moment Method.- Electrical Networks.- Infinite Networks.- The Method of Random Paths.- Transience of Percolation Clusters.- Subperiodic Trees.- The Random Walks RW (lambda) .- Capacity.-.Intersection-Equivalence.- Reconstruction for the Ising Model on a Tree,- Unpredictable Paths in Z and EIT in Z3.- Tree-Indexed Processes.- Recurrence for Tree-Indexed Markov Chains.- Dynamical Pecsolation.- Stochastic Domination Between Trees.

Пер. с англ. - М.: Мир, 1989. - 400 с. Автор (из США) излагает вопросы современной магнетохимии применительно главным образом к координационной химии переходных металлов. В краткой и доступной форме представлены подходы к магнетохимическому исследованию различных соединений переходных металлов и физической трактовке полученных результатов. Для химиков, физиков, физикохимиков, работающих в области неорганической химии и особенно координационной химии, аспирантов и студентов, специализирующихся в данных областях.

A crime that rocked a city. A case that stunned a nation. Based on the United States's first recorded murder trial, Eve Karlin's spellbinding debut novel re-creates early nineteenth-century New York City, where a love affair ends in a brutal murder and a conspiracy involving Alexander Hamilton and Aaron Burr erupts in shattering violence. It is high time to tell the truth. Time for justice. . . . How she was murdered and why she haunts me. It is not only Elma's story, it's mine. On the bustling docks of the Hudson River, Catherine Ring waits with her husband and children for the ship carrying her cousin, Elma Sands. Their Greenwich Street boardinghouse becomes a haven for Elma, who has at last escaped the stifling confines of her small hometown and the shameful circumstances of her birth. But in the summer of 1799, Manhattan remains a teeming cesspool of stagnant swamps and polluted rivers. The city is desperate for clean water as fires...

Farmacevtsko društvo Slovenije, 1964. В книге описаны словенские народные названия лекарственных растений и их примененеие.

October 2017, Front Cover Mathematics REsearch Communities Quantitative Linear Algebra Table of Contents Front matter The Rigidity of Frameworks: Theory and Applications by Jessica Sidman and Audrey St. John AMS Short Course Dido's Problem and Its Impact on Modern Mathematics by Catherine Bandle Call for Applications Associate Editor, Mathematical Reviews Ensuring That Mathematics is Relevant ina World of Data Science AMS Centennial Fellowship Fund Flexibility in the Mathematics Major Would benefit Students and Society Statistics on Women Mathematicians Euphemia Lofton Haynes, Bringing Education Closer to the Goal of Perfection" Call for Suggestions Evelyn Lamb Interview by Alexander Diaz-Lopez What is...? Perimeter by Frank Morgan Gerrymandering, Sandwiches, and Topology by Pablo Soberion. AMS Graduate Student Blog Free Shipping for AMS Members AMS Short Course IAS Membership A Formula Goes to Court: Partisan Gerrymandering and the Efficiency Gap by Mira Bernstein and Moon Duchin AMS on Social Networks Report of the Treasurer (2016) London Mathematical Society Inside the AMS Mathematics People Latinos and Hispanics int he Mathematical Sciences Mathematics Opportunities AMS Employment Center The Mathematician's Shiva, A Review by Dennis DeTurck Bookshelf The Back Page New Publications Offered by the AMS Classified Advertisements Mathematics Calendar Meetings & Conferences of the AMS October Table of Contents Meetings & Conferences of the AMS Program at a Glance AMS Dinner JMM Hotel Reservations JMM Advance REgistration/housing In the Next Issue Graduate Studies in Mathematics

Enjoy a great reading experience when you buy the Kindle edition of this book.Think clearly. Process your feelings. Make better decisions.We all strive to succeed in all areas of life and in the shortest possible time. But the biggest obstacle most of us encounter is our inability to persevere—in thought, path and process.The problem lies not in us, but in the fact that we don’t know how to deal with it properly.Turning Dreams into Reality is based on the PMCR (Physics of Magnetism Created Reality) method, developed by Yuval Tabib, a personal consultant and leading lecturer, that can make spiritual and personal growth much easier and more enjoyable, as we learn to understand our physical reality.It will give you simple, practical and well-paced tools, for just a few minutes at the beginning and end of the day, allowing you to work independently on your own through direct insights you can easily implement:How to easily be relieved of financial obstacles in a short time and feel the benefits of doing so.How to find “the one” who’s right for you without becoming frustrated every time.How to change your thoughts, awareness and subconscious.How to develop and use positive thinking to create dreams.How to relate to others and thus be loved by those around you.You are the basis for everything. With the right guidance you can make a change and grow to achieve the good, fulfilling life you always thought you deserved!

L'intrigue se déroule en grande partie de nos jours, quand le Professeur Adjemian est assassiné alors qu'il avait trouvé la réponse à la fondamentale question «D'où venons-nous?». La jeune journaliste Lucrèce Nemrod couvre l'affaire et décide de découvrir pourquoi le paléontologue a été tué alors même que la police classe l'affaire. Pour son article, Lucrèce demande de l'aide à Isidore Katzenberg, un ancien journaliste scientifique qui vit dans un château d'eau. Ce drôle de personnage partira avec sa collègue en Afrique pour tenter de percer le secret qui coûte la vie de plusieurs personnes tout au long du récit. Simultanément, une seconde intrigue s'entremêle avec l'enquête des deux journalistes. Cette seconde histoire se passe «Quelque part en Afrique de l'Est. Il y a 3,7 millions d'années.» et retrace la vie d'un homme des cavernes appelé tout simplement «IL».

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