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Exact Asymptotics of the Freezing Transition of a Logarithmically Correlated Random Energy Model

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Abstract

We consider a logarithmically correlated random energy model, namely a model for directed polymers on a Cayley tree, which was introduced by Derrida and Spohn. We prove asymptotic properties of a generating function of the partition function of the model by studying a discrete time analogy of the KPP-equation—thus translating Bramson’s work on the KPP-equation into a discrete time case. We also discuss connections to extreme value statistics of a branching random walk and a rescaled multiplicative cascade measure beyond the critical point.

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Authors and Affiliations

  1. Department of Mathematics, University of Helsinki, P.O. Box 4, 00014, Helsinki, Finland

    Christian Webb

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  1. Christian Webb
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Correspondence to Christian Webb.

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This research was funded by the Academy of Finland.

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Webb, C. Exact Asymptotics of the Freezing Transition of a Logarithmically Correlated Random Energy Model. J Stat Phys 145, 1595–1619 (2011). https://doi.org/10.1007/s10955-011-0359-8

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  • DOI: https://doi.org/10.1007/s10955-011-0359-8

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