文章基本信息

标题：Connectivity properties of random interlacement and intersection of random walks
本地全文：下载
作者：Balázs Ráth ; Artëm Sapozhnikov
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2012
卷号：IX
页码：67-83
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：We consider the interlacement Poisson point process on the space ofdoubly-infinite Zd-valued trajectories modulo time shift, tending to infinity at positiveand negative infinite times. The set of vertices and edges visited by at leastone of these trajectories is the random interlacement at level u of Sznitman (2010).We prove that for any u > 0, almost surely, (1) any two vertices in the randominterlacement at level u are connected via at most dd/2e trajectories of the pointprocess, and (2) there are vertices in the random interlacement at level u whichcan only be connected via at least dd/2e trajectories of the point process. In particular,this implies the already known result of Sznitman (2010) that the randominterlacement at level u is connected.
关键词：Random interlacement; random walk; intersection of random walks;capacity; Wiener test.