GREEDY LATTICE ANIMALS II: LINEAR GROWTH
成果类型：
Article
署名作者：
Gandolfi, Alberto; Kesten, Harry
署名单位：
University of California System; University of California Berkeley; Cornell University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/aoap/1177005201
发表日期：
1994
页码：
76-107
关键词：
摘要：
Let {X-v: v is an element of Z(d)} be i.i.d. positive random variables and define M-n = max{Sigma X-v is an element of pi(v) : pi a self-avoiding path of length n starting at the origin}, N-n = max{Sigma(v is an element of xi) X-v: xi a lattice animal of size n containing the origin}. In a preceding paper it was shown that if E{X-0(d)(log+ X-0)(d+a)) < infinity for some a > 0, then there exists some constant C such that w.p.1, 0 <= M-n <= N-n <= Cn for all large n. In this part we improve this result by showing that, in fact, there exist constants M, N < infinity such that w.p.1, M-n/n -> M and N-n/n -> N.