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Quenched tail estimate for the random walk in random scenery and in random layered conductance

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  • Deuschel, Jean-Dominique
  • Fukushima, Ryoki

Abstract

We discuss the quenched tail estimates for the random walk in random scenery. The random walk is the symmetric nearest neighbor walk and the random scenery is assumed to be independent and identically distributed, non-negative, and has a power law tail. We identify the long time asymptotics of the upper deviation probability of the random walk in quenched random scenery, depending on the tail of scenery distribution and the amount of the deviation. The result is in turn applied to the tail estimates for a random walk in random conductance which has a layered structure.

Suggested Citation

  • Deuschel, Jean-Dominique & Fukushima, Ryoki, 2019. "Quenched tail estimate for the random walk in random scenery and in random layered conductance," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 102-128.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:1:p:102-128
    DOI: 10.1016/j.spa.2018.02.011
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    References listed on IDEAS

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    1. Gantert, Nina & van der Hofstad, Remco & König, Wolfgang, 2006. "Deviations of a random walk in a random scenery with stretched exponential tails," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 480-492, March.
    2. Castell, F. & Pradeilles, F., 2001. "Annealed large deviations for diffusions in a random Gaussian shear flow drift," Stochastic Processes and their Applications, Elsevier, vol. 94(2), pages 171-197, August.
    3. Csáki, Endre & König, Wolfgang & Shi, Zhan, 1999. "An embedding for the Kesten-Spitzer random walk in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 283-292, August.
    4. Khoshnevisan, Davar & Lewis, Thomas M., 1998. "A law of the iterated logarithm for stable processes in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 74(1), pages 89-121, May.
    5. Chen, Xia, 2001. "Moderate deviations for Markovian occupation times," Stochastic Processes and their Applications, Elsevier, vol. 94(1), pages 51-70, July.
    6. Fleischmann, Klaus & Mörters, Peter & Wachtel, Vitali, 2008. "Moderate deviations for a random walk in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 118(10), pages 1768-1802, October.
    7. Asselah, A. & Castell, F., 2003. "Quenched large deviations for diffusions in a random Gaussian shear flow drift," Stochastic Processes and their Applications, Elsevier, vol. 103(1), pages 1-29, January.
    8. Zhang, Li-Xin, 2001. "The strong approximation for the Kesten-Spitzer random walk," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 21-26, May.
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    1. Andres, Sebastian & Croydon, David A. & Kumagai, Takashi, 2024. "Heat kernel fluctuations and quantitative homogenization for the one-dimensional Bouchaud trap model," Stochastic Processes and their Applications, Elsevier, vol. 172(C).

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