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Random walks in quenched i.i.d. space-time random environment are always a.s. diffusive
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  • Published: 02 February 2004

Random walks in quenched i.i.d. space-time random environment are always a.s. diffusive

  • C. Boldrighini1,
  • R.A. Minlos2 &
  • A. Pellegrinotti3 

Probability Theory and Related Fields volume 129, pages 133–156 (2004)Cite this article

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Abstract.

We consider a general model of discrete-time random walk X t on the lattice ν, ν = 1,..., in a random environment ξ={ξ(t,x):(t,x)∈ ν+1} with i.i.d. components ξ(t,x). Previous results on the a.s. validity of the Central Limit Theorem for the quenched model required a small stochasticity condition. In this paper we show that the result holds provided only that an obvious non-degeneracy condition is met. The proof is based on the analysis of a suitable generating function, which allows to estimate L 2 norms by contour integrals.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica G. Castelnuovo, Universitá ‘‘La Sapienza’‘, Piazzale Aldo Moro 5, 00185, Roma, Italy

    C. Boldrighini

  2. Institute for Problems of Information Transmission, Russian Academy of Sciences

    R.A. Minlos

  3. Dipartimento di Matematica, Universitá degli studi di Roma Tre, Largo San Leonardo Murialdo 1, 00146, Roma, Italy

    A. Pellegrinotti

Authors
  1. C. Boldrighini
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  2. R.A. Minlos
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  3. A. Pellegrinotti
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Additional information

Partially supported by C.N.R. (G.N.F.M.) and M.U.R.S.T. research funds.

Partially supported by C.N.R. (G.N.F.M.) and M.U.R.S.T. research funds, by R.F.F.I. grants n. 99-01-00284, 97-01-00714, and CRDF research funds N RM1-2085.

Partially supported by C.N.R. (G.N.F.M.) and M.U.R.S.T. research funds.

Mathematics Subject Classification (2000): 60J15, 60F05, 60G60, 82B41

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Boldrighini, C., Minlos, R. & Pellegrinotti, A. Random walks in quenched i.i.d. space-time random environment are always a.s. diffusive. Probab. Theory Relat. Fields 129, 133–156 (2004). https://doi.org/10.1007/s00440-003-0331-x

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  • Received: 30 November 2002

  • Revised: 06 November 2003

  • Published: 02 February 2004

  • Issue Date: May 2004

  • DOI: https://doi.org/10.1007/s00440-003-0331-x

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Key words or phrases

  • Random walk
  • Random Environment
  • Central Limit Theorem
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