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Almost sure estimates for the concentration neighborhood of Sinai's walk

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  • Andreoletti, Pierre

Abstract

We consider Sinai's random walk in random environment. We prove that infinitely often (i.o.) the size of the concentration neighborhood of this random walk is bounded almost surely. We also get that i.o. the maximal distance between two favorite sites is bounded almost surely.

Suggested Citation

  • Andreoletti, Pierre, 2007. "Almost sure estimates for the concentration neighborhood of Sinai's walk," Stochastic Processes and their Applications, Elsevier, vol. 117(10), pages 1473-1490, October.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:10:p:1473-1490
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    References listed on IDEAS

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    1. Andreoletti, Pierre, 2006. "On the concentration of Sinai's walk," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1377-1408, October.
    2. Kesten, Harry, 1986. "The limit distribution of Sinai's random walk in random environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 138(1), pages 299-309.
    3. Shi, Zhan, 1998. "A local time curiosity in random environment," Stochastic Processes and their Applications, Elsevier, vol. 76(2), pages 231-250, August.
    4. Gantert, Nina & Shi, Zhan, 2002. "Many visits to a single site by a transient random walk in random environment," Stochastic Processes and their Applications, Elsevier, vol. 99(2), pages 159-176, June.
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    Cited by:

    1. Grégoire Véchambre, 2023. "Almost Sure Behavior for the Local Time of a Diffusion in a Spectrally Negative Lévy Environment," Journal of Theoretical Probability, Springer, vol. 36(2), pages 876-925, June.
    2. Zindy, Olivier, 2008. "Upper limits of Sinai's walk in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 118(6), pages 981-1003, June.

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