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arXiv · 1603.01709

Subdiffusivity of a random walk among a Poisson system of moving traps on ${\mathbb Z}$

Siva Athreya·Alexander Drewitz·Rongfeng Sun
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Abstract

We consider a random walk among a Poisson system of moving traps on ${\mathbb Z}$. In earlier work [DGRS12], the quenched and annealed survival probabilities of this random walk have been investigated. Here we study the path of the random walk conditioned on survival up to time $t$ in the annealed case and show that it is subdiffusive. As a by-product, we obtain an upper bound on the number of so-called thin points of a one-dimensional random walk, as well as a bound on the total volume of the holes in the random walk's range.

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Siva Athreya, Alexander Drewitz, Rongfeng Sun. 2016-03-05. Subdiffusivity of a random walk among a Poisson system of moving traps on ${\mathbb Z}$. https://doi.org/10.1007/s11040-016-9227-8

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