Electronic Journal of Probability

Absolute continuity and weak uniform mixing of random walk in dynamic random environment

Stein Andreas Bethuelsen and Florian Völlering

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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.

Article information

Electron. J. Probab., Volume 21 (2016), paper no. 71, 32 pp.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 82C41: Dynamics of random walks, random surfaces, lattice animals, etc. [See also 60G50]
Secondary: 82C43: Time-dependent percolation [See also 60K35] 60F17: Functional limit theorems; invariance principles 60K37: Processes in random environments

random walk dynamic random environment absolute continuity stability central limit theorem hidden Markov models disagreement percolation

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Bethuelsen, Stein Andreas; Völlering, Florian. Absolute continuity and weak uniform mixing of random walk in dynamic random environment. Electron. J. Probab. 21 (2016), paper no. 71, 32 pp. doi:10.1214/16-EJP10. https://projecteuclid.org/euclid.ejp/1480688088

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