Convergence of the Law of the Environment Seen by the Particle for Directed Polymers in Random Media in the L <SUP>2</SUP> Region

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dc.contributor.authorMoreno, Gregorio
dc.date.accessioned2025-01-21T00:05:53Z
dc.date.available2025-01-21T00:05:53Z
dc.date.issued2010
dc.description.abstractWe consider the model of directed polymers in an i.i.d. Gaussian or bounded environment (Imbrie and Spencer in J. Stat. Phys. 52(3/4), 609-626, 1988; Carmona and Hu in Probab. Theory Relat. Fields 124(3), 431-457, 2002; Comets et al. in Adv. Stud. Pure Math. 39, 115-142, 2004) in the L (2) region. We prove the convergence of the law of the environment seen by the particle.
dc.description.abstractAs a main technical step, we establish a lower tail concentration inequality for the partition function for bounded environments. Our proof is based on arguments developed by Talagrand in the context of the Hopfield model (Talagrand in Probab. Theory Relat. Fields 110, 177-276, 1998). This improves in some sense a concentration inequality obtained by Carmona and Hu for Gaussian environments. We use this and a local limit theorem (Sinai in Fund. Math. 147, 173-180, 1995; Vargas in Ann. Inst. H. Poincar, Probab. Stat. 42(5), 521-534, 2006) to prove the L (1) convergence of the density of the law of the environment seen by the particle with respect to the product measure.
dc.fuente.origenWOS
dc.identifier.doi10.1007/s10959-008-0203-5
dc.identifier.issn0894-9840
dc.identifier.urihttps://doi.org/10.1007/s10959-008-0203-5
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/95566
dc.identifier.wosidWOS:000276901200008
dc.issue.numero2
dc.language.isoen
dc.pagina.final477
dc.pagina.inicio466
dc.revistaJournal of theoretical probability
dc.rightsacceso restringido
dc.subjectDirected polymers in random media
dc.subjectEnvironment seen by the particle
dc.subjectLimit theorems
dc.titleConvergence of the Law of the Environment Seen by the Particle for Directed Polymers in Random Media in the L <SUP>2</SUP> Region
dc.typeartículo
dc.volumen23
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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