The Annals of Applied Probability

The Bouchaud–Anderson model with double-exponential potential

S. Muirhead, R. Pymar, and R. S. dos Santos

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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.

Article information

Source
Ann. Appl. Probab., Volume 29, Number 1 (2019), 264-325.

Dates
Received: March 2018
Revised: July 2018
First available in Project Euclid: 5 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1544000430

Digital Object Identifier
doi:10.1214/18-AAP1417

Mathematical Reviews number (MathSciNet)
MR3910005

Zentralblatt MATH identifier
07039126

Subjects
Primary: 60H25: Random operators and equations [See also 47B80]
Secondary: 82C44: Dynamics of disordered systems (random Ising systems, etc.)

Keywords
Parabolic Anderson model Bouchaud trap model intermittency localisation

Citation

Muirhead, S.; Pymar, R.; dos Santos, R. S. The Bouchaud–Anderson model with double-exponential potential. Ann. Appl. Probab. 29 (2019), no. 1, 264--325. doi:10.1214/18-AAP1417. https://projecteuclid.org/euclid.aoap/1544000430


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