No more than three favorite sites for simple random walk
نویسندگان
چکیده
منابع مشابه
Favourite sites of simple random walk
We survey the current status of the list of questions related to the favourite (or: most visited) sites of simple random walk on Z, raised by Pál Erdős and Pál Révész in the early eighties.
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Let S(n) be a simple random walk taking values in Zd. A time n is called a cut time if S[0, n]∩ S[n+ 1,∞) = ∅. We show that in three dimensions the number of cut times less than n grows like n1−ζ where ζ = ζd is the intersection exponent. As part of the proof we show that in two or three dimensions P{S[0, n]∩ S[n+ 1, 2n] = ∅} n−ζ , where denotes that each side is bounded by a constant times the...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2001
ISSN: 0091-1798
DOI: 10.1214/aop/1008956341