文章基本信息

标题：Uniformity of hitting times of the contact process
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作者：Markus Heydenreich ; Christian Hirsch ; Daniel Valesin 等
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), dened for each site x as the rsttime at which it becomes infected. First, the family of random variables (t(x) 􀀀t(y))=jx􀀀yj, indexed by x 6= y in Zd, is stochastically tight. Second, for each " > 0there exists x such that, for innitely 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).
关键词：Contact process; coexistence; hitting times;