Show simple item record

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorPoisat, Julien
HAL ID: 6620
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorSimenhaus, François
dc.date.accessioned2022-02-25T15:11:47Z
dc.date.available2022-02-25T15:11:47Z
dc.date.issued2022
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22775
dc.language.isoenen
dc.subjectRandom walks in random obstaclesen
dc.subjectpolymers in random environmentsen
dc.subjectparabolic Anderson modelen
dc.subjectsurvival probabilityen
dc.subjectlocalizationen
dc.subjectone-city theoremen
dc.subjectMarkov renewal processesen
dc.subject.ddc519en
dc.titleLocalization of a one-dimensional simple random walk among power-law renewal obstaclesen
dc.typeDocument de travail / Working paper
dc.description.abstractenWe consider a one-dimensional simple random walk killed by quenched soft obstacles. The position of the obstacles is drawn according to a renewal process with a power-law increment distribution. In a previous work, we computed the large-time asymptotics of the quenched survival probability. In the present work we continue our study by describing the behaviour of the random walk conditioned to survive. We prove that with large probability, the walk quickly reaches a unique time-dependent optimal gap that is free from obstacle and gets localized there. We actually establish a dichotomy. If the renewal tail exponent is smaller than one then the walk hits the optimal gap and spends all of its remaining time inside, up to finitely many visits to the bottom of the gap. If the renewal tail exponent is larger than one then the random walk spends most of its time inside of the optimal gap but also performs short outward excursions, for which we provide matching upper and lower bounds on their length and cardinality. Our key tools include a Markov renewal interpretation of the survival probability as well as various comparison arguments for obstacle environments. Our results may also be rephrased in terms of localization properties for a directed polymer among multiple repulsive interfaces.en
dc.publisher.cityParisen
dc.identifier.citationpages55en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris Dauphine-PSLen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-03526023en
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.identifier.citationdate2022
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2022-02-25T15:09:34Z
hal.author.functionaut
hal.author.functionaut


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record