
Intersections of Random Walks
Gregory F. Lawler(Author)
Birkhauser Boston Inc (Publisher)
Published on 1. September 1991
Book
Hardback
IV, 220 pages
978-0-8176-3557-2 (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.
More details
Series
Edition
1991
Language
English
Place of publication
MA
United States
Target group
College/higher education
Professional and scholarly
Research
Illustrations
IV, 220 p.
Dimensions
Height: 0 mm
Width: 0 mm
Weight
490 gr
ISBN-13
978-0-8176-3557-2 (9780817635572)
DOI
10.1007/978-1-4757-2137-9
Schweitzer Classification
Other editions
Additional editions

Gregory F. Lawler
Intersections of Random Walks
Book
09/1992
Birkhauser
€85.59
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Previous edition
Gregory F. Lawler
Intersections of Random Walks
Book
1991
Birkhäuser Verlag GmbH
€73.04
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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.