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- W4301870140 abstract "Consider the model where particles are initially distributed on $mathbb{Z}^d, , dgeq 2$, according to a Poisson point process of intensity $lambda>0$, 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 $mathbb{Z}^d, , dgeq 2$, 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. We consider the case where the target can move with speed at most 1, according to any continuous function and can adapt its motion based on the location of the particles. We show that there exists sufficiently small $lambda_* > 0$, so that if the initial density of particles $lambda < lambda_*$, then the target can avoid detection forever." @default.
- W4301870140 created "2022-10-05" @default.
- W4301870140 creator A5013068717 @default.
- W4301870140 creator A5086138992 @default.
- W4301870140 date "2013-12-30" @default.
- W4301870140 modified "2023-10-18" @default.
- W4301870140 title "Phase transition for finite-speed detection among moving particles" @default.
- W4301870140 doi "https://doi.org/10.48550/arxiv.1312.7862" @default.
- W4301870140 hasPublicationYear "2013" @default.
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