ON A GENERAL MANY-DIMENSIONAL EXCITED RANDOM WALK

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dc.contributor.authorMenshikov, Mikhail
dc.contributor.authorPopov, Serguei
dc.contributor.authorRamirez, Alejandro F.
dc.contributor.authorVachkovskaia, Marina
dc.date.accessioned2024-01-10T13:15:44Z
dc.date.available2024-01-10T13:15:44Z
dc.date.issued2012
dc.description.abstractIn this paper we study a substantial generalization of the model of excited random walk introduced in [Electron. Commun. Probab. 8 (2003) 86-92] by Benjamini and Wilson. We consider a discrete-time stochastic process (X-n, n = 0, 1, 2, ...) taking values on Z(d), d >= 2, described as follows: when the particle visits a site for the first time, it has a uniformly-positive drift in a given direction l; when the particle is at a site which was already visited before, it has zero drift. Assuming uniform ellipticity and that the jumps of the process are uniformly bounded, we prove that the process is ballistic in the direction l so that lim inf(n ->infinity) X-n.l/n > 0. A key ingredient in the proof of this result is an estimate on the probability that the process visits less than n(1/2+alpha) distinct sites by time n, where a is some positive number depending on the parameters of the model. This approach completely avoids the use of tan points and coupling methods specific to the excited random walk. Furthermore, we apply this technique to prove that the excited random walk in an i.i.d. random environment satisfies a ballistic law of large numbers and a central limit theorem.
dc.description.funderMecesup
dc.description.funderCNPq
dc.description.funderFAPESP
dc.description.funderFondo Nacional de Desarrollo Cientifico y Tecnologico
dc.fechaingreso.objetodigital2024-05-15
dc.format.extent25 páginas
dc.fuente.origenWOS
dc.identifier.doi10.1214/11-AOP678
dc.identifier.issn0091-1798
dc.identifier.urihttps://doi.org/10.1214/11-AOP678
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/78526
dc.identifier.wosidWOS:000311005600008
dc.information.autorucMatemática;Ramirez A;S/I;70094
dc.issue.numero5
dc.language.isoen
dc.nota.accesocontenido completo
dc.pagina.final2130
dc.pagina.inicio2106
dc.publisherINST MATHEMATICAL STATISTICS
dc.revistaANNALS OF PROBABILITY
dc.rightsacceso abierto
dc.subjectExcited random walk
dc.subjectcookie random walk
dc.subjecttransience
dc.subjectballisticity
dc.subjectrange
dc.subjectINTEGERS
dc.subjectTRANSIENCE
dc.subjectRECURRENCE
dc.titleON A GENERAL MANY-DIMENSIONAL EXCITED RANDOM WALK
dc.typeartículo
dc.volumen40
sipa.codpersvinculados70094
sipa.indexWOS
sipa.indexScopus
sipa.trazabilidadCarga SIPA;09-01-2024
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