Two Problems about Random Walks in a Random Field of Traps

#### M.V. Menshikov, S.E. Volkov, F. den Hollander

1995, v.1, №2, 185-202

ABSTRACT

This paper is about simple random walks on $Z^d$, $d \ge 3$, in a random field of traps, the density of which tends to zero at infinity. We distinguish between the quenched problem (when the traps are fixed) and the annealed problem (when the traps are updated each unit of time). Our goal is not only to find a criterion for zero vs. positive probability of survival, but also to show three different methods that can be applied in this area. These methods are based on Lyapunov functions, capacity and mean hitting time respectively.

Keywords: simple random walk,random field of traps,Lyapunov function,capacity,Wiener's test,annealed problem,quenched problem