Complete Localisation and Exponential Shape of the Parabolic Anderson Model with Weibull Potential Field
View/ Open
Volume
19
Pagination
1 - 27
Publisher
Journal
Electronic Journal of Probability
ISSN
1083-6489
Metadata
Show full item recordAbstract
We consider the parabolic Anderson model with Weibull potential field, for all values of the Weibull parameter. We prove that the solution is eventually localised at a single site with overwhelming probability (complete localisation) and, moreover, that the solution has exponential shape around the localisation site. We determine the localisation site explicitly, and derive limit formulae for its distance, the profile of the nearby potential field and its ageing behaviour. We also prove that the localisation site is determined locally, that is, by maximising a certain time-dependent functional that depends only on: (i) the value of the potential field in a neighbourhood of fixed radius around a site; and (ii) the distance of that site to the origin.
Authors
Fiodorov, A; Muirhead, SCollections
- Mathematics [1421]