Random walks in mobile trap environments in Z d

Abstract:  We consider a random walk among a Poisson cloud of moving traps on ��Zd, where the walk is killed at a rate proportional to the number of traps occupying the same position. In dimension �=1d=1, it is known that the annealed law of the random walk conditioned on survival up to time �t is sub-diffusive. In this talk we show that in large enough dimension, this annealed law satisfies an invariance principle under diffusive scaling. Our proof is based on the theory of thermodynamic formalism, where we extend some classic results for Markov shifts with a potential of summable variation and a finite alphabet to the case of an uncountable non-compact alphabet. This is joint work with Alex Drewitz and Rongfeng Sun