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


Fukushima, R (2009). From the Lifshitz tail to the quenched survival asymptotics in the trapping problem. Electronic Communications in Probability, 14:435-446.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2009
Deposited On:13 Feb 2010 11:28
Last Modified:24 Sep 2019 16:41
Publisher:University of Washington
ISSN:1083-589X
OA Status:Green
Publisher DOI:https://doi.org/10.1214/ECP.v14-1497
Official URL:http://www.emis.de/journals/EJP-ECP/_ejpecp/index-2.html
Related URLs:http://arxiv.org/abs/0905.4436

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