Brownian motion with absorption in a clusterized random medium (Q1363963)

We study the problem of Brownian motion with absorption in a microscopically inhomogeneous correlated random medium, in which spatial correlations have a selective character, resulting in the grouping of traps into clusters. We consider a very simple model, assuming these clusters to have the same stochastic structure, stochastically independent of each other, and assuming that these clusters do not interact, i.e., that they are distributed by the Poisson law [see the authors, \textit{A. M. Berezhkovskij} and \textit{S. A. Molchanov}, Phys. Rev. E 47, No. 6, 4564-4567 (1993)]. We show that in this model there is a slowdown effect in the destruction process, and we obtain asymptotics similar to the law of \textit{M. D. Donsker} and \textit{S. R. S. Varadhan} [Commun. Pure Appl. Math. 28, 525-565 (1975; Zbl 0333.60077)] for the survival probability.