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

Author

Listed:
  • Ryoki Fukushima

    (Tokyo Institute of Technology
    Kyoto University)

  • Naoki Kubota

    (Nihon University)

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.

Suggested Citation

  • Ryoki Fukushima & Naoki Kubota, 2014. "Quenched Large Deviations for Multidimensional Random Walk in Random Environment with Holding Times," Journal of Theoretical Probability, Springer, vol. 27(4), pages 1140-1166, December.
    • Handle: RePEc:spr:jotpro:v:27:y:2014:i:4:d:10.1007_s10959-013-0514-z
    DOI: 10.1007/s10959-013-0514-z
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    References listed on IDEAS

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    1. Flury, Markus, 2007. "Large deviations and phase transition for random walks in random nonnegative potentials," Stochastic Processes and their Applications, Elsevier, vol. 117(5), pages 596-612, May.
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