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An intersection property of the simple random walks inZ d

An intersection property of the simple random walks inZ d Let {S d (n)} n≥0 be the simple random walk inZ d , and Π(d)(a,b)={S d (n)∈Z d :a≤n≤b}. Supposef(n) is an integer-valued function and increases to infinity asn tends to infinity, andE n (d) ={Π(d)(0,n)∩Π(d)(n+f(n),∞)≠∅}. In this paper, a necessary and sufficient condition to ensureP(E n d) ,i.o.)=0, or 1 is derived ford=3, 4. This problem was first studied by P. Erdös and S.J. Taylor. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

An intersection property of the simple random walks inZ d

Acta Mathematicae Applicatae Sinica , Volume 12 (2) – Jul 13, 2005

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References (8)

Publisher
Springer Journals
Copyright
Copyright © 1996 by Science Press
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02007735
Publisher site
See Article on Publisher Site

Abstract

Let {S d (n)} n≥0 be the simple random walk inZ d , and Π(d)(a,b)={S d (n)∈Z d :a≤n≤b}. Supposef(n) is an integer-valued function and increases to infinity asn tends to infinity, andE n (d) ={Π(d)(0,n)∩Π(d)(n+f(n),∞)≠∅}. In this paper, a necessary and sufficient condition to ensureP(E n d) ,i.o.)=0, or 1 is derived ford=3, 4. This problem was first studied by P. Erdös and S.J. Taylor.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 13, 2005

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