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Title of Journal: J Stat Phys

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Abbravation: Journal of Statistical Physics

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Springer US

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DOI

10.1002/cber.188301602259

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1572-9613

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A Class of Random Walks in Reversible Dynamic Envi

Authors: Luca Avena Oriane Blondel Alessandra Faggionato
Publish Date: 2016/08/24
Volume: 165, Issue: 1, Pages: 1-23
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Abstract

We introduce via perturbation a class of random walks in reversible dynamic environments having a spectral gap In this setting one can apply the mathematical results derived in Avena et al L2Perturbed Markov processes and applications to random walks in dynamic random environments Preprint 2016 As first results we show that the asymptotic velocity is antisymmetric in the perturbative parameter and for a subclass of random walks we characterize the velocity and a stationary distribution of the environment seen from the walker as suitable series in the perturbative parameter We then consider as a special case a random walk on the East model that tends to follow dynamical interfaces between empty and occupied regions We study the asymptotic velocity and density profile for the environment seen from the walker In particular we determine the sign of the velocity when the density of the underlying East process is not 1 / 2 and we discuss the appearance of a drift in the balanced setting given by density 1 / 2The following lemma is a consequence of reversibility and the orientation property of the East model which we use to prove Proposition 42 We write mathbb E mathrmeast eta for the expectation of the East dynamics starting at eta and we define mathbb E mathrmeast nu rho similarly

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