Brownian Survival Among Gibbsian Traps

Abstract

We consider Brownian motion evolving among killing traps. We develop a technique of "enlargement of obstacles." This technique allows us to replace given trap configurations by configurations of enlarged traps, when deriving upper estimates on the probability that Brownian motion survives. Applied in a context of random obstacles, this reduces the complexity of the description for the environment seen by Brownian motion. We apply the method to the case where traps are distributed according to a fairly general Gibbs measure and obtain a result in the spirit of Donsker-Varadhan's theorem on Wiener sausage asymptotics.