Cut Times for Simple Random Walk
نویسندگان
چکیده
منابع مشابه
Cut times for Simple Random Walk Cut times for Simple Random Walk
Let S(n) be a simple random walk taking values in Z d. A time n is called a cut time if S0; n] \ Sn + 1; 1) = ;: We show that in three dimensions the number of cut times less than n grows like n 1? where = d is the intersection exponent. As part of the proof we show that in two or three dimensions PfS0; n] \ Sn + 1; 2n] = ;g n ? ; where denotes that each side is bounded by a constant times the ...
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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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A cut time for a Brownian motion or a random walk is a time at which the past and the future of the process to not intersect. In this paper we review the work of Erdős on cut times and discuss more recent work on in this area. 1 Erdős and cut times Let Bt be a Brownian motion taking values in R, and let Sn be a simple random walk taking values in Z. A cut time is a time such that the paths of t...
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 1996
ISSN: 1083-6489
DOI: 10.1214/ejp.v1-13