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The limit distribution of Sinai's random walk in random environment

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  • Kesten, Harry

Abstract

Recently Sinai proved that if {Xn is a one-dimensional random walk in random environment which is recurrent, then (log n)-2Xn converges in distribution. Here we calculate the limit distribution explicitly.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:138:y:1986:i:1:p:299-309
    DOI: 10.1016/0378-4371(86)90186-X
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    Citations

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    Cited by:

    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. Shi, Zhan, 1998. "A local time curiosity in random environment," Stochastic Processes and their Applications, Elsevier, vol. 76(2), pages 231-250, August.
    3. Diel, Roland, 2011. "Almost sure asymptotics for the local time of a diffusion in Brownian environment," Stochastic Processes and their Applications, Elsevier, vol. 121(10), pages 2303-2330, October.
    4. Hu, Yueyun, 2000. "Tightness of localization and return time in random environment," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 81-101, March.
    5. 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.
    6. Buraczewski, Dariusz & Dyszewski, Piotr & Iksanov, Alexander & Marynych, Alexander, 2020. "Random walks in a strongly sparse random environment," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 3990-4027.
    7. Menshikov, M.V. & Wade, Andrew R., 2008. "Logarithmic speeds for one-dimensional perturbed random walks in random environments," Stochastic Processes and their Applications, Elsevier, vol. 118(3), pages 389-416, March.

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