Subdiffusivity of a Random Walk Among a Poisson System of Moving Traps on ℤ
Mathematical Physics Analysis and Geometry
We consider a random walk among a Poisson system of moving traps on 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.
Athreya, Siva; Drewitz, Alexander; and Sun, Rongfeng, "Subdiffusivity of a Random Walk Among a Poisson System of Moving Traps on ℤ" (2017). Journal Articles. 2669.