Abstract
We consider a random walk among a Poisson system of moving traps on \(\mathbb {Z}\). In earlier work (Drewitz et al. Springer Proc. Math. 11, 119-158 2012), 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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Athreya, S., Drewitz, A. & Sun, R. Subdiffusivity of a Random Walk Among a Poisson System of Moving Traps on \(\mathbb {Z}\) . Math Phys Anal Geom 20, 1 (2017). https://doi.org/10.1007/s11040-016-9227-8
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DOI: https://doi.org/10.1007/s11040-016-9227-8
Keywords
- Parabolic anderson model
- Random walk in random potential
- Trapping dynamics
- Subdiffusive
- Thin points of a random walk