Weak quenched limiting distributions for transient one-dimensional random walk in a random environment

Peterson, Jonathon
Samorodnitsky, Gennady

Publication date

December 2010

Abstract

We consider a one-dimensional, transient random walk in a random i.i.d. environment. The asymptotic behaviour of such random walk depends to a large extent on a crucial parameter kappa>0 that determines the fluctuations of the process. When 0<kappa<2, the averaged distributions of the hitting times of the random walk converge to a kappa-stable distribution. However, it was shown recently that in this case there does not exist a quenched limiting distribution of the hitting times. That is, it is not true that for almost every fixed environment, the distributions of the hitting times (centered and scaled in any manner) converge to a non-degenerate distribution. We show, however, that the quenched distributions do have a limit in th...

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Weak quenched limiting distributions for transient one-dimensional random walk in a random environment

Abstract

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Weak quenched limiting distributions for transient one-dimensional random walk in a random environment

Abstract

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