Phase transition for finite-speed detection among moving particles

Vladas Sidoravicius, A Stauffer

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Abstract

Consider the model where particles are initially distributed on Zd,d≥2, according to a Poisson point process of intensity λ>0, and are moving in continuous time as independent simple symmetric random walks. We study the escape versus detection problem, in which the target, initially placed at the origin of Zd,d≥2, and changing its location on the lattice in time according to some rule, is said to be detected if at some finite time its position coincides with the position of a particle. For any given S>0S>0, we consider the case where the target can move with speed at most SS, according to any continuous function and can adapt its motion based on the location of the particles. We show that, for any S>0, there exists a sufficiently small λ∗>0, so that if the initial density of particles λ<λ∗, then the target can avoid detection forever.
Original languageEnglish
Pages (from-to)362-370
Number of pages9
JournalStochastic Processes and their Applications
Volume125
Issue number1
Early online date17 Sep 2014
DOIs
Publication statusPublished - Jan 2015

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Phase Transition
Phase transitions
Target
Poisson Point Process
Continuous Time
Random walk
Continuous Function
Motion
Model

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Phase transition for finite-speed detection among moving particles. / Sidoravicius, Vladas; Stauffer, A.

In: Stochastic Processes and their Applications, Vol. 125, No. 1, 01.2015, p. 362-370.

Research output: Contribution to journalArticle

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