Muirhead, S;
Pymar, R;
Sidorova, N;
(2017)
Delocalising the parabolic Anderson model through partial duplication of the potential.
Probability Theory and Related Fields
, 171
(3-4)
pp. 917-979.
10.1007/s00440-017-0798-5.
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Abstract
The parabolic Anderson model on Zd 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.
| Type: | Article |
|---|---|
| Title: | Delocalising the parabolic Anderson model through partial duplication of the potential |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00440-017-0798-5 |
| Publisher version: | https://doi.org/10.1007/s00440-017-0798-5 |
| Language: | English |
| Additional information: | 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. |
| Keywords: | Science & Technology, Physical Sciences, Statistics & Probability, Mathematics, Parabolic Anderson model, Localisation, Intermittency, INTERMITTENCY, LOCALIZATION |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1520057 |
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