Quenched Large Deviations for Multidimensional Random Walk in Random Environment with Holding Times

Ryoki Fukushima () and Naoki Kubota
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Ryoki Fukushima: Tokyo Institute of Technology
Naoki Kubota: Nihon University

Journal of Theoretical Probability, 2014, vol. 27, issue 4, 1140-1166

Abstract: Abstract We consider a random walk in random environment with random holding times, that is, the random walk jumping to one of its nearest neighbors with some transition probability after a random holding time. Both the transition probabilities and the laws of the holding times are randomly distributed over the integer lattice. Our main result is a quenched large deviation principle for the position of the random walk. The rate function is given by the Legendre transform of the so-called Lyapunov exponents for the Laplace transform of the first passage time. By using this representation, we derive some asymptotics of the rate function in some special cases.

Keywords: Random walk in random environment; Holding times; Large deviations; 60K37; 60F10 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10959-013-0514-z

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