Random walks in quenched i.i.d. space-time random environment are always a.s. diffusive
type: Item
instance of: scholarly article
title: Random walks in quenched i.i.d. space-time random environment are always a.s. diffusive
zbMATH Open document ID: 1062.60044
publication date: 2004-10-28T00:00:00Z
review text: The authors deal with a general model of random walk \(X_t\) on the \(\gamma\)-dimensional lattice \(\mathbb Z^\gamma\) in a random environment \(\xi=\{\xi(t,x): (t,x)\in \mathbb Z^{\gamma+1}\}\) with i.i.d. components taking values in some space \(S\) and distributed according to a non-degenerate probability measure \(\pi\). The random walk transition probabilities satisfy \[ P(X_{t+1} = y \mid X_t = x,\xi ) = P_0(y-x) + c (y-x;\xi) \] where \(\{P_0(u): u\in \mathbb Z^\gamma\}\) are the transition probabilities of a homogeneous completely irreducible random walk with the restriction that for all \(u \in \mathbb Z^\gamma\), \(E[c(u;\;\;)]=0\). It is further assumed that \(P_0\) and \(c\) go to zero at \(\infty\): \[ \sum_{u\in Z^\gamma} \Bigl\{P_0(u)+\sup_s |c(u,s)|\Bigr\}e^{d|u|}<\infty. \] Under some further conditions, the authors establish the central limit theorem and also show that the environment does not affect the limit distribution.
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 82B41
zbMATH DE Number: 2111539
author: C. Boldrighini
author: R. A. Minlos
author: A. Pellegrinotti
MaRDI profile type: Publication
full work available at URL: s00440-003-0331-x
OpenAlex ID: W1977723846
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DOI: 10.1007/S00440-003-0331-X
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 2111539