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The survival problem for a diffusing particle moving among random traps isconsidered. We introduce a simple argument to derive the quenched asymptoticsof the survival probability from the Lifshitz tail effect for the associatedoperator. In particular, the upper bound is proved in fairly general settingsand is shown to be sharp in the case of the Brownian motion in the Poissonianobstacles. As an application, we derive the quenched asymptotics for theBrownian motion in traps distributed according to a random perturbation of thelattice.

From the Lifshitz tail to the quenched survival asymptotics in the trapping problem