From the Lifshitz tail to the quenched survival asymptotics in the trapping problem. (English) Zbl 1191.60122

Summary: The survival problem for a diffusing particle moving among random traps is considered. We introduce a simple argument to derive the quenched asymptotics of the survival probability from the Lifshitz tail effect for the associated operator. In particular, the upper bound is proved in fairly general settings and is shown to be sharp in the case of the Brownian motion among Poissonian obstacles. As an application, we derive the quenched asymptotics for the Brownian motion among traps distributed according to a random perturbation of the lattice.


60K37 Processes in random environments
82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
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