On the delocalized phase of the random pinning model

2010/10/22 by Jean-Christophe Mourrat, Mourrat, Jean-Christophe
Mathematics · Physics and Astronomy · #60K37 #82B44 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60K37 #msc:82B44

paper · pdf · doi:10.48550/arxiv.1010.4671

4 pages

arxiv created 2010/10/22 · openalex publication_date 2010/10/22 · arxiv updated 2010/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 c log(n) tends to 0 as n tends to infinity. Our proofs rely on recent results of Birkner, Greven, den Hollander (2010) and Cheliotis, den Hollander (2010).

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