期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2013
卷号：X
期号：2
页码：813-829
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：Let the nodes of a Poisson point process move independently in Rdaccording to Brownian motions. We study the isolation time for a target particlethat is placed at the origin, namely how long it takes until there is no node of thePoisson point process within distance r of it. In the case when the target particledoes not move, we obtain asymptotics for the tail probability which are tight up toconstants in the exponent in dimension d 3 and tight up to logarithmic factorsin the exponent for dimensions d = 1; 2. In the case when the target particle isallowed to move independently of the Poisson point process, we show that the beststrategy for the target to avoid isolation is to stay put.
