The infinite valley for a recurrent random walk in random environment

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dc.creatorGantert, Nina
dc.creatorPeres, Yuval
dc.creatorShi, Zhan
dc.date2007-08-13
dc.date2009-02-26
dc.date.accessioned2026-07-07T12:46:24Z
dc.date.available2026-07-07T12:46:24Z
dc.descriptionWe consider a one-dimensional recurrent random walk in random environment (RWRE). We show that the - suitably centered - empirical distributions of the RWRE converge weakly to a certain limit law which describes the stationary distribution of a random walk in an infinite valley. The construction of the infinite valley goes back to Golosov. As a consequence, we show weak convergence for both the maximal local time and the self-intersection local time of the RWRE and also determine the exact constant in the almost sure upper limit of the maximal local time.
dc.description17 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/0708.1739
dc.identifierhttp://arxiv.org/abs/0708.1739
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/221368
dc.subjectProbability
dc.subject60K37, 60J50, 60J55, 60F10
dc.titleThe infinite valley for a recurrent random walk in random environment
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