Moscow Mathematical Journal

Volume 16, Issue 4, October–December 2016 pp. 621–640.

Random Walk in Dynamic Random Environment with Long-Range Space Correlations

Authors: C. Boldrighini (1), R. A. Minlos (2), and A. Pellegrinotti (3)
Author institution:(1) Istituto Nazionale di Alta Matematica (INdAM), unità locale Dipartimento di Matematica e Fisica, Università di Roma Tre, Largo S. Leonardo Murialdo 1, 00146 Rome, Italy
(2) Institute for Problems of Information Transmission, Russian Academy of Sciences
(3) Dipartimento di Matematica e Fisica, Università di Roma Tre, Largo S. Leonardo Murialdo 1, 00146 Rome, Italy

Summary:

Models of random walks (RW) in dynamic random environment (RE) are usually considered under some space-time mixing conditions with sufficient decay. We study a discrete-time model on ℤ in an environment independent in time, but with non-absolutely summable space correlations. We show that an a.-s. quenched Central Limit Theorem (CLT) holds, with the same leading term as in the uncorrelated case, and the same order of decay of the first correction. Some conclusions are drawn on the type of correlations that could modify the leading terms of the CLT asymptotics.

2010 Math. Subj. Class. 60J10, 60K37, 82B41.

Keywords: Random walks, random environment, central limit theorem, correlations.

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