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    Delocalising the Parabolic Anderson Model through partial duplication of the potential

    Muirhead, S. and Pymar, Richard and 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. ISSN 0178-8051.

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    Abstract

    The parabolic Anderson model on 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.

    Metadata

    Item Type: Article
    Additional Information: The final publication is available at Springer via the link above.
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Dr Richard Pymar
    Date Deposited: 04 Sep 2017 13:07
    Last Modified: 27 Jul 2018 14:41
    URI: http://eprints.bbk.ac.uk/id/eprint/19506

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