Path properties of the disordered pinning model in the delocalized regime

Abstract

We study the path properties of a random polymer attracted to a defect line by a potential with disorder, and we prove that in the delocalized regime, at any temperature, the number of contacts with the defect line remains in a certain sense "tight in probability" as the polymer length varies. On the other hand we show that at sufficiently low temperature, there exists a.s. a subsequence where the number of contacts grows like the log of the length of the polymer.

Published in at http://dx.doi.org/10.1214/13-AAP930 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (9)

• Fractional moment bounds and disorder relevance for pinning models
• Marginal relevance of disorder for pinning models
• A replica-coupling approach to disordered pinning models
• Pinning of polymers and interfaces by random potentials
• Disordered pinning models and copolymers: beyond annealed bounds
• Estimates on path delocalization for copolymers at selective interfaces
• Quenched and Annealed Critical Points in Polymer Pinning Models
• Variational characterization of the critical curve for pinning of random polymers
• Equality of critical points for polymer depinning transitions with loop exponent one

Cited by in corpus (3)

• Pinning on a defect line: characterization of marginal disorder relevance and sharp asymptotics for the critical point shift
• Localization, big-jump regime and the effect disorder for a class of generalized pinning models
• Pinning and disorder relevance for the lattice Gaussian Free Field II: the two dimensional case