Research

Ageing in the parabolic Anderson model


Reference:

Morters, P., Ortgiese, M. and Sidorova, N., 2011. Ageing in the parabolic Anderson model. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 47 (4), pp. 969-1000.

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    Official URL:

    http://dx.doi.org/10.1214/10-AIHP394

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    Abstract

    The parabolic Anderson model is the Cauchy problem for the heat equation with a random potential. We consider this model in a setting which is continuous in time and discrete in space, and focus on time-constant, independent and identically distributed potentials with polynomial tails at infinity. We are concerned with the long-term temporal dynamics of this system. Our main result is that the periods, in which the profile of the solutions remains nearly constant, are increasing linearly over time, a phenomenon known as ageing. We describe this phenomenon in the weak sense, by looking at the asymptotic probability of a change in a given time window, and in the strong sense, by identifying the almost sure upper envelope for the process of the time remaining until the next change of profile. We also prove functional scaling limit theorems for profile and growth rate of the solution of the parabolic Anderson model.

    Details

    Item Type Articles
    CreatorsMorters, P., Ortgiese, M. and Sidorova, N.
    DOI10.1214/10-AIHP394
    Related URLs
    URLURL Type
    http://arxiv.org/abs/0910.5613Free Full-text
    DepartmentsFaculty of Science > Mathematical Sciences
    Publisher Statementageing.pdf: The authors reserve the right to "The right to place the final version of this article (exactly as published in the journal) on their own homepage or in a public digital repository, provided there is a link to the official journal site." See: http://imstat.org/aihp/
    RefereedYes
    StatusPublished
    ID Code26549

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