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 Mosc. Math. J.: Year: Volume: Issue: Page: Find

 Mosc. Math. J., 2016, Volume 16, Number 4, Pages 621–640 (Mi mmj612)

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

Abstract: 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.

 Funding Agency Grant Number Istituto Nazionale di Alta Matematica "Francesco Severi" M.U.R.S.T. Sapienza Università di Roma Russian Foundation for Basic Research 14-01-00379 The first named author supported in part by research funds of INdAM (G.N.F.M.), M.U.R.S.T. and Università di Roma “La Sapienza”. The second named author supported in part by RFFI grant N 14-01-00379. The third named author supported in part by Research Funds of INdAM (GNFM), MURST and Università Roma Tre.

DOI: https://doi.org/10.17323/1609-4514-2016-16-4-621-640

Full text: http://www.mathjournals.org/.../2016-016-004-002.html
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Bibliographic databases:

MSC: 60J10, 60K37, 82B41
Received: November 18, 2015; in revised form March 15, 2016
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Citation: 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
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