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2016 Absolute continuity and weak uniform mixing of random walk in dynamic random environment
Stein Andreas Bethuelsen, Florian Völlering
Electron. J. Probab. 21: 1-32 (2016). DOI: 10.1214/16-EJP10


We prove results for random walks in dynamic random environments which do not require the strong uniform mixing assumptions present in the literature. We focus on the “environment seen from the walker"-process and in particular its invariant law. Under general conditions it exists and is mutually absolutely continuous to the environment law. With stronger assumptions we obtain for example uniform control on the density or a quenched CLT. The general conditions are made more explicit by looking at hidden Markov models or Markov chains as environment and by providing simple examples.


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Stein Andreas Bethuelsen. Florian Völlering. "Absolute continuity and weak uniform mixing of random walk in dynamic random environment." Electron. J. Probab. 21 1 - 32, 2016.


Received: 10 February 2016; Accepted: 17 October 2016; Published: 2016
First available in Project Euclid: 2 December 2016

zbMATH: 1355.82042
MathSciNet: MR3580037
Digital Object Identifier: 10.1214/16-EJP10

Primary: 82C41
Secondary: 60F17 , 60K37 , 82C43

Keywords: Absolute continuity , central limit theorem , disagreement percolation , Dynamic random environment , Hidden Markov models , Random walk , stability


Vol.21 • 2016
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