Quenched Large Deviations for Multidimensional Random Walk in Random Environment with Holding Times |
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Authors: | Ryoki Fukushima Naoki Kubota |
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Affiliation: | 1. Department of Mathematics, Tokyo Institute of Technology, Tokyo, 152-8551, Japan 2. Research Institute of Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan 3. Department of Mathematics, Graduate School of Science and Technology, Nihon University, Tokyo, 101-8308, Japan
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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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