Delocalising the parabolic Anderson model through partial duplication of the potential
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Volume
171
Pagination
917 - 979
Publisher
Journal
Probability Theory and Related Fields
Issue
ISSN
0178-8051
Metadata
Show full item recordAbstract
The parabolic Anderson model on $\mathbb{Z}^d$ with i.i.d. potential is known to completely localise if the distribution of the potential is sufficiently heavy-tailed at infinity. In this paper we investigate a modification of the model in which the potential is partially duplicated in a symmetric way across a plane through the origin. In the case of potential distribution with polynomial tail decay, we exhibit a surprising phase transition in the model as the decay exponent varies. For large values of the exponent the model completely localises as in the i.i.d. case. By contrast, for small values of the exponent we show that the model may delocalise. More precisely, we show that there is an event of non-negligible probability on which the solution has non-negligible mass on two sites.
Authors
Muirhead, S; Pymar, R; Sidorova, NCollections
- Mathematics [1439]