
Intersections of Random Walks
Gregory F. Lawler(Author)
Birkhauser Boston Inc (Publisher)
Published on 28. August 1996
Book
Paperback/Softback
IV, 225 pages
978-0-8176-3892-4 (ISBN)
Description
A more accurate title for this book would be "Problems dealing with the non-intersection of paths of random walks. " These include: harmonic measure, which can be considered as a problem of nonintersection of a random walk with a fixed set; the probability that the paths of independent random walks do not intersect; and self-avoiding walks, i. e. , random walks which have no self-intersections. The prerequisite is a standard measure theoretic course in probability including martingales and Brownian motion. The first chapter develops the facts about simple random walk that will be needed. The discussion is self-contained although some previous expo sure to random walks would be helpful. Many of the results are standard, and I have made borrowed from a number of sources, especially the ex cellent book of Spitzer [65]. For the sake of simplicity I have restricted the discussion to simple random walk. Of course, many of the results hold equally well for more general walks. For example, the local central limit theorem can be proved for any random walk whose increments have mean zero and finite variance. Some of the later results, especially in Section 1. 7, have not been proved for very general classes of walks. The proofs here rely heavily on the fact that the increments of simple random walk are bounded and symmetric.
Reviews / Votes
"Much of the material is Lawler's own research, so he knows his story thoroughly and tells it well."
-SIAM Review
More details
Series
Edition
1991 ed.
Language
English
Place of publication
Boston
United States
Target group
Professional and scholarly
Research
Illustrations
IV, 225 p.
Dimensions
Height: 279 mm
Width: 210 mm
Thickness: 13 mm
Weight
577 gr
ISBN-13
978-0-8176-3892-4 (9780817638924)
DOI
10.1007/978-1-4612-0771-9
Schweitzer Classification
Other editions
Previous edition
Gregory F. Lawler
Intersections of Random Walks
Book
08/1996
Birkhäuser Verlag GmbH
€33.43
Article exhausted; check different version
Content
1 Simple Random Walk.- 2 Harmonic Measure.- 3 Intersection Probabilities.- 4 Four Dimensions.- 5 Two and Three Dimensions.- 6 Self-Avoiding Walks.- 7 Loop-Erased Walk.