dc.contributor.author | Muirhead, S | en_US |
dc.contributor.author | Pymar, R | en_US |
dc.contributor.author | Sidorova, N | en_US |
dc.date.accessioned | 2018-10-25T09:48:21Z | |
dc.date.issued | 2017-09-06 | en_US |
dc.date.submitted | 2018-10-15T15:36:22.634Z | |
dc.identifier.issn | 0178-8051 | en_US |
dc.identifier.uri | http://qmro.qmul.ac.uk/xmlui/handle/123456789/48763 | |
dc.description | Published version. 39 pages, 1 figure | en_US |
dc.description | Published version. 39 pages, 1 figure | en_US |
dc.description | Published version. 39 pages, 1 figure | en_US |
dc.description | Published version. 39 pages, 1 figure | en_US |
dc.description.abstract | 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. | en_US |
dc.format.extent | 917 - 979 | en_US |
dc.publisher | Springer Verlag | en_US |
dc.relation.ispartof | Probability Theory and Related Fields | en_US |
dc.rights | This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. | |
dc.subject | math.PR | en_US |
dc.subject | math.PR | en_US |
dc.title | Delocalising the parabolic Anderson model through partial duplication of the potential | en_US |
dc.type | Article | |
dc.rights.holder | © The Author(s) 2017 | |
pubs.author-url | http://arxiv.org/abs/1609.07421v2 | en_US |
pubs.issue | 3-4 | en_US |
pubs.notes | Not known | en_US |
pubs.publication-status | Published | en_US |
pubs.volume | 171 | en_US |