A random walk on Z with drift driven by its occupation time at zero

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dc.creatorBen-Ari, Iddo
dc.creatorMerle, Mathieu
dc.creatorRoitershtein, Alexander
dc.date2007-11-30
dc.date.accessioned2026-07-07T08:46:23Z
dc.date.available2026-07-07T08:46:23Z
dc.descriptionWe consider a nearest neighbor random walk on the one-dimensional integer lattice with drift towards the origin determined by an asymptotically vanishing function of the number of visits to zero. We show the existence of distinct regimes according to the rate of decay of the drift. In particular, when the rate is sufficiently slow, the position of the random walk, properly normalized, converges to a symmetric exponential law. In this regime, in contrast to the classical case, the range of the walk scales differently from its position.
dc.identifierhttps://arxiv.org/abs/0711.4871
dc.identifierhttp://arxiv.org/abs/0711.4871
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/143231
dc.subjectProbability
dc.subject60F17, 60F20, 60F5
dc.titleA random walk on Z with drift driven by its occupation time at zero
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