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Precise large deviation estimates for a one-dimensional random walk in a random environment
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  • Published: February 1999

Precise large deviation estimates for a one-dimensional random walk in a random environment

  • Agoston Pisztora1,
  • Tobias Povel2 &
  • Ofer Zeitouni3 

Probability Theory and Related Fields volume 113, pages 191–219 (1999)Cite this article

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ωx

} (taking values in the interval [1/2, 1)), which serve as an environment. This environment defines a random walk {X k } (called a RWRE) which, when at x, moves one step to the right with probability ω x , and one step to the left with probability 1 −ωx. Solomon (1975) determined the almost-sure asymptotic speed (= rate of escape) of a RWRE, in a more general set-up. Dembo, Peres and Zeitouni (1996), following earlier work by Greven and den Hollander (1994) on the quenched case, have computed rough tail asymptotics for the empirical mean of the annealed RWRE. They conjectured the form of the rate function in a full LDP. We prove in this paper their conjecture. The proof is based on a “coarse graining scheme” together with comparison techniques.

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Authors and Affiliations

  1. Department of Mathematics, Harvard University, Cambridge MA 02138, USA, , , , , , US

    Agoston Pisztora

  2. Department of Mathematics, M.I.T. Present address: Wängistr. 3, CH-8142 Uitikon, Switzerland (e-mail: tobias.povel@zurich.com), , , , , , CH

    Tobias Povel

  3. Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel, , , , , , IL

    Ofer Zeitouni

Authors
  1. Agoston Pisztora
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  2. Tobias Povel
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  3. Ofer Zeitouni
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Received: 22 July 1997/Revised version: 15 June 1998

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Pisztora, A., Povel, T. & Zeitouni, O. Precise large deviation estimates for a one-dimensional random walk in a random environment. Probab Theory Relat Fields 113, 191–219 (1999). https://doi.org/10.1007/s004400050206

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  • Issue Date: February 1999

  • DOI: https://doi.org/10.1007/s004400050206

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  • Mathematics Subject Classification (1991): J15, F10, C44, J80
  • Key words: Random walk in random environment – Large deviations
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