作者：Gladkich, Alexey; Peled, Ron
作者单位：Tel Aviv University
摘要：We study the length of cycles of random permutations drawn from the Mallows distribution. Under this distribution, the probability of a permutation pi is an element of S-n is proportional to q(inv(pi)) where q > 0 and inv(pi) is the number of inversions in pi. We focus on the case that q < 1 and show that the expected length of the cycle containing a given point is of order min{(1 - q)(-2), n}. This marks the existence of two asymptotic regimes: with high probability, when n tends to infinity ...
作者：Shiraishi, Daisuke
作者单位：Kyoto University
摘要：Let M-n be the number of steps of the loop- erasure of a simple random walk on Z(3) run until its first exit from a ball of radius n. In the paper, we will show the existence of the growth exponent, that is, we show that there exists beta > 0 such that (n ->infinity)lim log E (M-n)/log n = beta.
