BROWNIAN SURVIVAL IN A CLUSTERIZED TRAPPING MEDIUM

The survival problem for a Brownian particle moving among random traps is considered in the case where the traps are correlated in a particu lar fashion being gathered in clusters. It is assumed that the cluster s are statistically identical and independent of each other and are di stributed in space according to a Poisson law. Mathematically, such a trapping medium is described via a Poisson cluster point process. We p rove that the particle survival probability is increased at all times as compared to the case of noncorrelated (Poissonian) traps, which imp lies the slowdown of the trapping process. It is shown that this effec t may be interpreted as the manifestation of the trap ''attraction'', thus supporting assertions on the qualitative influence of the trap '' interaction'' on the trapping rate claimed earlier in the physical lit erature. The long-time survival asymptotics (of Donsker-Varadhan type) is also derived. By way of appendix, FKG inequalities for certain fun ctionals are proven and the limiting distribution for a Poisson cluste r process, under clusters' scaling, is determined.