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Random walks in random environment: What a single trajectory tells

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Abstract

We present a procedure that determines the law of a random walk in an iid random environment as a function of a single “typical” trajectory. We indicate when the trajectory characterizes the law of the environment, and we say how this law can be determined. We then show how independent trajectories having the distribution of the original walk can be generated as functions of the single observed trajectory.

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Authors and Affiliations

  1. Laboratoire de Probabilités et Modèles Aléatoires, Université Paris 6, 4 place Jussieu, 75252, Paris cedex 05, France

    Omer Adelman & Nathanaël Enriquez

Authors
  1. Omer Adelman
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  2. Nathanaël Enriquez
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Correspondence to Omer Adelman.

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Adelman, O., Enriquez, N. Random walks in random environment: What a single trajectory tells. Isr. J. Math. 142, 205–220 (2004). https://doi.org/10.1007/BF02771533

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  • DOI: https://doi.org/10.1007/BF02771533

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