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 Electronic Communications in Probability > Vol. 14 (2009) > Paper 42 open journal systems 


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

Ryoki Fukushima, University of Zurich


Abstract
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.


Full text: PDF

Pages: 435-446

Published on: October 6, 2009
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