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Large deviations and wandering exponent for random walk in a dynamic beta environment

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)2186-2229
Number of pages47
JournalAnnals of Probability
Volume47
Issue number4
Early online date4 Jul 2019
DOIs
DateAccepted/In press - 10 Aug 2018
DateE-pub ahead of print - 4 Jul 2019
DatePublished (current) - Jul 2019

Abstract

Random walk in a dynamic i.i.d. beta random environment, conditioned to escape at an atypical velocity, converges to a Doob transform of the original walk. The Doob-transformed environment is correlated in time, i.i.d.\ in space, and its marginal density function is a product of a beta density and a hypergeometric function. Under its averaged distribution the transformed walk obeys the wandering exponent 2/3 that agrees with Kardar-Parisi-Zhang universality. The harmonic function in the Doob transform comes from a Busemann-type limit and appears as an extremal in a variational problem for the quenched large deviation rate function.

    Research areas

  • Hypergeometric function, Beta distribution, Doob transform, Wandering exponent, RWRE, Random walk, Random environment, Large deviations, KPZ, Kardar-Parisi-Zhang equation

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  • Full-text PDF (accepted author manuscript)

    Rights statement: This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Project Euclid at https://projecteuclid.org/euclid.aop/1562205707 . Please refer to any applicable terms of use of the publisher.

    Accepted author manuscript, 554 KB, PDF document

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