The Annals of Probability

Random walk in Markovian environment

Dmitry Dolgopyat, Gerhard Keller, and Carlangelo Liverani

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We prove a quenched central limit theorem for random walks with bounded increments in a randomly evolving environment on ℤd. We assume that the transition probabilities of the walk depend not too strongly on the environment and that the evolution of the environment is Markovian with strong spatial and temporal mixing properties.

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Ann. Probab., Volume 36, Number 5 (2008), 1676-1710.

First available in Project Euclid: 11 September 2008

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Zentralblatt MATH identifier

Primary: 60K37: Processes in random environments
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60F05: Central limit and other weak theorems 37H99: None of the above, but in this section 82B41: Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41] 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)

Central limit theorem random walk random environment Markov process


Dolgopyat, Dmitry; Keller, Gerhard; Liverani, Carlangelo. Random walk in Markovian environment. Ann. Probab. 36 (2008), no. 5, 1676--1710. doi:10.1214/07-AOP369.

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