On the delocalized phase of the random pinning model

TL;DR

This paper investigates the delocalized phase of a directed polymer model with random charges, showing the boundedness of the partition function and that the number of contact points grows slower than logarithmically for almost all environments.

Contribution

It establishes boundedness of the partition function and characterizes the growth rate of contact points in the delocalized phase, extending understanding of the model's behavior.

Findings

Partition function remains bounded in the delocalized phase.

Number of contact points grows slower than c log(n) for almost all environments.

Results rely on recent advances in related probabilistic models.

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).