期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2018
卷号：XV
期号：1
页码：233-245
DOI：10.30757/ALEA.v15-11
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：For the supercritical contact process on the hyper-cubic lattice startedfrom a single infection at the origin and conditioned on survival, we establish twouniformity results for the hitting times t(x), de ned for each site x as the rsttime at which it becomes infected. First, the family of random variables (t(x) t(y))=jxyj, indexed by x 6= y in Zd, is stochastically tight. Second, for each " > 0there exists x such that, for in nitely many integers n, t(nx) < t((n + 1)x) withprobability larger than 1 ". A key ingredient in our proofs is a tightness resultconcerning the essential hitting times of the supercritical contact process introducedby Garet and Marchand (2012).
