Intersections of Random Walks

Gregory F. Lawler

ISBN 10: 081763892X / ISBN 13: 9780817638924

Editore: Birkhäuser, Birkhäuser, 1996

Riguardo questo articolo

Druck auf Anfrage Neuware - Printed after ordering - 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.

Codice articolo 9780817638924

Dati bibliografici

• Titolo: Intersections of Random Walks
• Editore: Birkhäuser, Birkhäuser
• Data di pubblicazione: 1996
• Lingua: Inglese
• ISBN 10: 081763892X
• ISBN 13: 9780817638924
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 279 L x 210 A x 13 P (millimetri) 279 millimetri di larghezza per 210 millimetri di altezza per 13 millimetri di profondità
• Peso: 577 grammi

Descrizione articolo

Riassunto

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.

Recensione

"Much of the material is Lawler’s own research, so he knows his story thoroughly and tells it well."

―SIAM Review