On the delocalized phase of the random pinning model

Jean Christophe Mourrat

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider the model of a directed polymer pinned to a line of i.i.d. random charges, and focus on the interior of the delocalized phase. We first show that in this region, the partition function remains bounded. We then prove that for almost every environment of charges, the probability that the number of contact points in [0, n] exceeds clogn tends to 0 as n tends to infinity. The proofs rely on recent results of Birkner, Greven, den Hollander (2010) and Cheliotis, den Hollander (2010).

Original languageEnglish (US)
Title of host publicationSeminaire de Probabilites XLIV
PublisherSpringer Verlag
Pages401-407
Number of pages7
ISBN (Print)9783642274602
DOIs
StatePublished - 2012

Publication series

NameLecture Notes in Mathematics
Volume2046
ISSN (Print)0075-8434

ASJC Scopus subject areas

  • Algebra and Number Theory

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  • Cite this

    Mourrat, J. C. (2012). On the delocalized phase of the random pinning model. In Seminaire de Probabilites XLIV (pp. 401-407). (Lecture Notes in Mathematics; Vol. 2046). Springer Verlag. https://doi.org/10.1007/978-3-642-27461-9_18