THE BOUCHAUD–ANDERSON MODEL WITH DOUBLE-EXPONENTIAL POTENTIAL

The Bouchaud–Anderson model (BAM) is a generalisation of the parabolic and erson 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 dou...

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Bibliographic Details
Published in:The Annals of applied probability 2019-02, Vol.29 (1), p.264-325
Main Authors: Muirhead, S., Pymar, R., dos Santos, R. S.
Format: Article
Language:English
Subjects:
Algorithms
Binomial distribution
Position (location)
Random walk
Statistics
Trapping
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Summary:The Bouchaud–Anderson model (BAM) is a generalisation of the parabolic and erson 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.
ISSN:1050-5164
2168-8737
DOI:10.1214/18-AAP1417