An exponential upper bound for the survival probability in a dynamic random trap model

Abstract

We consider a symmetric translation-invariant random walk on thed-dimensional lattice ℤ^d. The walker moves in an environment of moving traps. When the walker hits a trap, he is killed. The configuration of traps in the course of time is a reversible Markov process satisfying a level-2 large-deviation principle. Under some restrictions on the entropy function, we prove an exponential upper bound for the survival probability, i.e.,

$$\mathop {lim sup}\limits_{t \to \infty } \frac{1}{t}\log \mathbb{P}(T \geqslant t)< 0$$

whereT is the survival time of the walker. As an example, our results apply to a random walk in an environment of traps that perform a simple symmetric exclusion process.