Cut Times for Simple Random Walk

Gregory Lawler
1996 Electronic Journal of Probability  
Let S(n) be a simple random walk taking values in Z d . 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 n 1−ζ where ζ = ζ d is the intersection exponent. As part of the proof we show that in two or three dimensions where denotes that each side is bounded by a constant times the other side.
doi:10.1214/ejp.v1-13 fatcat:twbiqe2pvvd75n3bnjzi33reue