Intersections of Random Walks

ISBN-13: 9781461459712 / Angielski / Miękka / 2012 / 223 str.

Gregory F. Lawler

Opis

A central study in Probability Theory is the behavior of fluctuation phenomena of partial sums of different types of random variable. One of the most useful concepts for this purpose is that of the random walk which has applications in many areas, particularly in statistical physics and statistical chemistry. Originally published in 1991, Intersections of Random Walks focuses on and explores a number of problems dealing primarily with the nonintersection of random walks and the self-avoiding walk. Many of these problems arise in studying statistical physics and other critical phenomena. Topics include: discrete harmonic measure, including an introduction to diffusion limited aggregation (DLA); the probability that independent random walks do not intersect; and properties of walks without self-intersections. The presentsoftcover reprint includes corrections andaddenda fromthe1996 printing, andmakesthis classic monographavailable to a wider audience. With a self-contained introduction to the properties of simple random walks, and an emphasis on rigorous results, the book will be useful to researchers in probability and statistical physics and to graduate students interested in basic properties of random walks.

Recenzje

...the text is extremely readable and informative.

-The Bulletin of Mathematics Books

Much of the material is Lawler's own research, so he knows his story thoroughly and tells it well.

-SIAM Review

...a very welcome presentation of the subject, serving as a central reference and source of information.

-Metrika

Spis treści

Simple Random Walk.- Harmonic Measure.- Intersection Probabilities.- Four Dimensions.- Two and Three Dimensions.- Self-Avoiding Walks.- Loop-Erased walk.- Recent Results.