Random walks in quenched i.i.d. space-time random environment are always a.s. diffusive
We consider a general model of discrete-time random walk Xt 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...
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Published in | Probability theory and related fields Vol. 129; no. 1; pp. 133 - 156 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Heidelberg
Springer Nature B.V
01.05.2004
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Subjects | |
Online Access | Get full text |
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Summary: | We consider a general model of discrete-time random walk Xt 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 L2 norms by contour integrals. |
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ISSN: | 0178-8051 1432-2064 |
DOI: | 10.1007/s00440-003-0331-x |