Random walk in dynamic random environment with long-range space correlations
C. Boldrighiniab, R. A. Minlosc, A. Pellegrinottib
a Istituto Nazionale di Alta Matematica (INdAM)
b Dipartimento di Matematica e Fisica, Università di Roma Tre, Largo S. Leonardo Murialdo 1, 00146 Rome, Italy
c Institute for Problems of Information Transmission, Russian Academy of Sciences
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 $\mathbb Z$ 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.
Key words and phrases:
random walks, random environment, central limit theorem, correlations.
MSC: 60J10, 60K37, 82B41
Received: November 18, 2015; in revised form March 15, 2016
C. Boldrighini, R. A. Minlos, A. Pellegrinotti, “Random walk in dynamic random environment with long-range space correlations”, Mosc. Math. J., 16:4 (2016), 621–640
Citation in format AMSBIB
\by C.~Boldrighini, R.~A.~Minlos, A.~Pellegrinotti
\paper Random walk in dynamic random environment with long-range space correlations
\jour Mosc. Math.~J.
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