Moment asymptotics for the parabolic Anderson problem with a perturbed lattice potential

The parabolic Anderson problem with a random potential obtained by attaching a long tailed potential around a randomly perturbed lattice is studied. The moment asymptotics of the total mass of the solution is derived. The results show that the total mass of the solution concentrates on a small set i...

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Bibliographic Details
Published inJournal of functional analysis Vol. 260; no. 3; pp. 724 - 744
Main Authors Fukushima, Ryoki, Ueki, Naomasa
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.02.2011
Subjects
Brownian motion
Parabolic Anderson problem
Perturbed lattice
Random media
Brownian motion
Perturbed lattice
Parabolic Anderson problem
Random media
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Summary:The parabolic Anderson problem with a random potential obtained by attaching a long tailed potential around a randomly perturbed lattice is studied. The moment asymptotics of the total mass of the solution is derived. The results show that the total mass of the solution concentrates on a small set in the space of configuration.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2010.10.016