Intersections of Random Walks
By: by Gregory F. Lawler
Contributors: SpringerLink (Online service)
Series: Modern Birkhäuser Classics
Publisher: Springer New York; Imprint: Birkhäuser
Published: 2013
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 223
ISBN-13: 9781461459729
Subjects: Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences; Mathematics; Distribution (Probability theory); Probability Theory and Stochastic Processes; Dynamical Systems and Complexity Statistical Physics
Description: <p>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. </p><p>Originally published in 1991, <i>Intersections of Random Walks</i> 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. </p><p>The present softcover reprint includes corrections and addenda from the 1996 printing, and  makes this classic monograph available 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.</p>
Table of contents: title: Simple Random Walk; title: Harmonic Measure; title: Intersection Probabilities; title: Four Dimensions; title: Two and Three Dimensions.- Self-Avoiding Walks.- Loop-Erased walk; title: Recent Results.