Quenched large deviations for multidimensional random walk in random environment with holding times

Ryoki Fukushima; Naoki Kubota

doi:10.1007/s10959-013-0514-z

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arXiv · 1202.5643

Quenched large deviations for multidimensional random walk in random environment with holding times

Ryoki Fukushima·Naoki Kubota

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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.

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BibTeX RIS

Ryoki Fukushima, Naoki Kubota. 2013-09-06. Quenched large deviations for multidimensional random walk in random environment with holding times. https://doi.org/10.1007/s10959-013-0514-z

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