A note on random walk in random scenery

2005/01/05 by Amine Asselah, Asselah, Amine, Fabienne Castell +1 · 1 citation
Computer Science · Mathematics · #Data Management and Algorithms #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #math.PR #msc:60F10 #msc:60J55 #msc:60K37

paper · pdf · doi:10.48550/arxiv.math/0501068

13 pages

arxiv created 2005/01/05 · arxiv updated 2009/12/01

Abstract

We consider a d-dimensional random walk in random scenery X(n), where the scenery consists of i.i.d. with exponential moments but a tail decay of the form exp(-c t^a) with a<d/2. We study the probability, when averaged over both randomness, that X(n)>ny. We show that this probability is of order exp(-(ny)^b) with b=a/(a+1).

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