Electronic Communications in Probability

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

Ryoki Fukushima

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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.

Article information

Source
Electron. Commun. Probab., Volume 14 (2009), paper no. 42, 435-446.

Dates
Accepted: 6 October 2009
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465234751

Digital Object Identifier
doi:10.1214/ECP.v14-1497

Mathematical Reviews number (MathSciNet)
MR2551853

Zentralblatt MATH identifier
1191.60122

Subjects
Primary: 60K37: Processes in random environments
Secondary: 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)

Keywords
Trapping problem random media survival probability Lifshitz tail

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Fukushima, Ryoki. From the Lifshitz tail to the quenched survival asymptotics in the trapping problem. Electron. Commun. Probab. 14 (2009), paper no. 42, 435--446. doi:10.1214/ECP.v14-1497. https://projecteuclid.org/euclid.ecp/1465234751


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