A quenched limit theorem for the local time of random walks on

Jürgen Gärtner and Rongfeng Sun

Stochastic Processes and their Applications, 2009, vol. 119, issue 4, 1198-1215

Abstract: Let X and Y be two independent random walks on with zero mean and finite variances, and let Lt(X,Y) be the local time of X-Y at the origin at time t. We show that almost surely with respect to Y, Lt(X,Y)/logt conditioned on Y converges in distribution to an exponential random variable with the same mean as the distributional limit of Lt(X,Y)/logt without conditioning. This question arises naturally from the study of the parabolic Anderson model with a single moving catalyst, which is closely related to a pinning model.

Keywords: Local; time; Random; walks; Quenched; exponential; law (search for similar items in EconPapers)
Date: 2009
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