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This book focuses on and explores a number of problems dealing primarily with the non-intersection 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.§With the inclusion of a self-contained introduction to the properties of simple random walk, and an emphasis in rigorous results, the book will be useful to researchers in probability and statistical physics and to graduate students interested in basic properties of random walk.
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