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Probability and Its Applications

Intersections of Random Walks

Authors: Lawler, Gregoyr

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About this book

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.

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $79.99
price for USA in USD
  • ISBN 978-1-4757-2137-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Intersections of Random Walks
Authors
Series Title
Probability and Its Applications
Copyright
1991
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-1-4757-2137-9
DOI
10.1007/978-1-4757-2137-9
Series ISSN
2297-0371
Edition Number
1
Number of Pages
IV, 220
Topics