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

Gregorio Moreno ()
Additional contact information
Gregorio Moreno: Université Paris 7

Journal of Theoretical Probability, 2010, vol. 23, issue 2, 466-477

Abstract: Abstract We 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. As 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. Poincaré 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.

Keywords: Directed polymers in random media; Environment seen by the particle; Limit theorems; 60K37; 60F05; 82B44 (search for similar items in EconPapers)
Date: 2010
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-008-0203-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:23:y:2010:i:2:d:10.1007_s10959-008-0203-5

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-008-0203-5

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().