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Large deviations and phase transition for random walks in random nonnegative potentials

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  • Flury, Markus

Abstract

We establish large deviation principles and phase transition results for both quenched and annealed settings of nearest-neighbor random walks with constant drift in random nonnegative potentials on . We complement the analysis of M.P.W. Zerner [Directional decay of the Green's function for a random nonnegative potential on , Ann. Appl. Probab. 8 (1996) 246-280], where a shape theorem on the Lyapunov functions and a large deviation principle in absence of the drift are achieved for the quenched setting.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:5:p:596-612
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    Cited by:

    1. Wiegel, Gundelinde Maria, 2018. "The relation between quenched and annealed Lyapunov exponents in random potential on trees," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 1988-2006.
    2. 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.

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