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February 2019 The Bouchaud–Anderson model with double-exponential potential
S. Muirhead, R. Pymar, R. S. dos Santos
Ann. Appl. Probab. 29(1): 264-325 (February 2019). DOI: 10.1214/18-AAP1417

Abstract

The Bouchaud–Anderson model (BAM) is a generalisation of the parabolic Anderson model (PAM) in which the driving simple random walk is replaced by a random walk in an inhomogeneous trapping landscape; the BAM reduces to the PAM in the case of constant traps. In this paper, we study the BAM with double-exponential potential. We prove the complete localisation of the model whenever the distribution of the traps is unbounded. This may be contrasted with the case of constant traps (i.e., the PAM), for which it is known that complete localisation fails. This shows that the presence of an inhomogeneous trapping landscape may cause a system of branching particles to exhibit qualitatively distinct concentration behaviour.

Citation

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S. Muirhead. R. Pymar. R. S. dos Santos. "The Bouchaud–Anderson model with double-exponential potential." Ann. Appl. Probab. 29 (1) 264 - 325, February 2019. https://doi.org/10.1214/18-AAP1417

Information

Received: 1 March 2018; Revised: 1 July 2018; Published: February 2019
First available in Project Euclid: 5 December 2018

zbMATH: 07039126
MathSciNet: MR3910005
Digital Object Identifier: 10.1214/18-AAP1417

Subjects:
Primary: 60H25
Secondary: 82C44

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 1 • February 2019
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