Journal article

The Bouchaud–Anderson model with double-exponential potential

S Muirhead, R Pymar, RS Dos Santos

Annals of Applied Probability | Institute of Mathematical Statistics | Published : 2019

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 c..

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University of Melbourne Researchers

Grants

Awarded by Engineering and Physical Sciences Research Council (EPSRC)


Awarded by EPSRC


Awarded by German DFG


Awarded by DFG


Funding Acknowledgements

Supported by the Engineering and Physical Sciences Research Council (EPSRC) Fellowship EP/M002896/1 held by Dmitry Belyaev.Supported in part by the EPSRC Grant EP/M027694/1 held by Codina Cotar.Supported by the German DFG project KO 2205/13 "Random mass flows through random potential" held by Wolfgang Konig, and by the DFG Research Unit FOR2402 "Rough paths, stochastic partial differential equations and related topics".