Open Access
July 2020 Random walks on dynamical random environments with nonuniform mixing
Oriane Blondel, Marcelo R. Hilário, Augusto Teixeira
Ann. Probab. 48(4): 2014-2051 (July 2020). DOI: 10.1214/19-AOP1414


In this paper, we study random walks on dynamical random environments in $1+1$ dimensions. Assuming that the environment is invariant under space-time shifts and fulfills a mild mixing hypothesis, we establish a law of large numbers and a concentration inequality around the asymptotic speed. The mixing hypothesis imposes a polynomial decay rate of covariances on the environment with sufficiently high exponent but does not impose uniform mixing. Examples of environments for which our methods apply include the contact process and Markovian environments with a positive spectral gap, such as the East model. For the East model, we also obtain that the distinguished zero satisfies a law of large numbers with strictly positive speed.


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Oriane Blondel. Marcelo R. Hilário. Augusto Teixeira. "Random walks on dynamical random environments with nonuniform mixing." Ann. Probab. 48 (4) 2014 - 2051, July 2020.


Received: 1 May 2018; Revised: 1 September 2019; Published: July 2020
First available in Project Euclid: 20 July 2020

zbMATH: 07224967
MathSciNet: MR4124532
Digital Object Identifier: 10.1214/19-AOP1414

Primary: 60G55 , 60K35 , 82B43

Keywords: dynamic random environments , Random walks , renormalization , Strong law of large numbers

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 4 • July 2020
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