树和网络上的概率 Probability on Trees and Networks 英文原版 Russell Lyons 概率论与数理统计

基本信息

Format:Hardback 720 pages, Worked examples or Exercises; 4 Tables, black and white; 13 Line drawings, color; 78 Line

Publisher:Cambridge University Press

Imprint:Cambridge University Press

ISBN:9781107160156

Published:20 Jan 2017

Classifications:Probability & statistics

Readership:Professional & Vocational Tertiary Education (US: College)

Weight:1416g

Dimensions:187 x 261 x 46 (mm)

书籍信息仅供参考，具体以实物为准

书籍简介

大约从20世纪50年代末开始，一些研究团体开始将图的几何学与这些图上的随机过程联系起来。这本书历时20年，将该领域的研究联系在一起，其中包括关于渗滤、等效不等式、特征值、过渡概率和随机漫步的工作。该书由两位领先的研究人员撰写，强调直觉，同时给出完整的证明和850多个练习。

书中讨论了许多近期的发展，作者在其中发挥了主导作用，包括树和Cayley图上的渗滤、均匀生成森林、质量运输技术，以及图上随机行走与希尔伯特空间嵌入的联系。这本关于网络概率的先进的书对研究生和研究人员来说都是不可缺少的。

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.

作者简介

罗素-里昂是布卢明顿印第安纳大学的James H. Rudy数学教授。他于1983年在密歇根大学获得博士学位。他撰写了关于树上概率和网络中随机生成树的开创性论文。里昂曾是斯隆基金会研究员，并曾是国际数学家大会和联合数学会议的特邀发言人。他是美国数学学会的会员。

尤瓦尔-佩雷斯是华盛顿州雷德蒙市微软研究院的首席研究员。他于1990年在耶路撒冷希伯来大学获得博士学位，后来在该大学和加州大学伯克利分校任教。他在概率、遍历理论、分析和理论计算机科学方面撰写了250多篇研究论文。他与人合著了关于布朗运动和马尔科夫链混合时间的书籍。佩雷斯于1995年获得罗洛-戴维森奖，2001年获得勒夫奖，2011年获得大卫-P-罗宾斯奖，并在2002年国际数学大会上担任特邀发言人。他是美国数学学会的研究员和美国国家科学院的外籍准会员。

Russell Lyons is James H. Rudy Professor of Mathematics at Indiana University, Bloomington. He obtained his PhD at the University of Michigan in 1983. He has written seminal papers concerning probability on trees and random spanning trees in networks. Lyons was a Sloan Foundation Fellow and has been an Invited Speaker at the International Congress of Mathematicians and the Joint Mathematics Meetings. He is a Fellow of the American Mathematical Society.

Yuval Peres is a Principal Researcher at Microsoft Research in Redmond, Washington. He obtained his PhD at the Hebrew University, Jerusalem in 1990 and later served on their faculty as well as on the faculty at the University of California, Berkeley. He has written more than 250 research papers in probability, ergodic theory, analysis, and theoretical computer science. He has coauthored books on Brownian motion and Markov chain mixing times. Peres was awarded the Rollo Davidson Prize in 1995, the Loève Prize in 2001, and the David P. Robbins Prize in 2011 and was an Invited Speaker at the 2002 ICM. He is a fellow of the American Mathematical Society and a foreign associate member of the US National Academy of Sciences.