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Anomalous behaviour for the random corrections to the cumulants of random walks in fluctuating random media
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  • Published: March 2001

Anomalous behaviour for the random corrections to the cumulants of random walks in fluctuating random media

  • M.S. Bernabei1 

Probability Theory and Related Fields volume 119, pages 410–432 (2001)Cite this article

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Abstract.

The Central Limit Theorem for a model of discrete-time random walks on the lattice ℤν in a fluctuating random environment was proved for almost-all realizations of the space-time nvironment, for all ν > 1 in [BMP1] and for all ν≥ 1 in [BBMP]. In [BMP1] it was proved that the random correction to the average of the random walk for ν≥ 3 is finite. In the present paper we consider the cases ν = 1,2 and prove the Central Limit Theorem as T→∞ for the random correction to the first two cumulants. The rescaling factor for theaverage is for ν = 1 and (ln T), for ν=2; for the covariance it is , ν = 1,2.

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Authors and Affiliations

  1. Dipartimento di Matematica e Fisica, Universitá di Camerino, Via Madonna delle Carceri, 9, 62032 Camerino, Italy. e-mail: bernabei@wiener.iam.uni-bonn.de, , , , , , IT

    M.S. Bernabei

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  1. M.S. Bernabei
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Received: 25 November 1999 / Revised version: 7 June 2000 / Published online: 15 February 2001

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Bernabei, M. Anomalous behaviour for the random corrections to the cumulants of random walks in fluctuating random media. Probab Theory Relat Fields 119, 410–432 (2001). https://doi.org/10.1007/PL00008765

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  • Issue Date: March 2001

  • DOI: https://doi.org/10.1007/PL00008765

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  • Mathematics Subject Classification (2000): 60J15, 60F05, 60G60, 82B41
  • Key words or phrases: Random walk – Random environment – Central Limit Theorem
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