The Annals of Applied Probability

Disordered pinning models and copolymers: Beyond annealed bounds

Fabio Lucio Toninelli

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We consider a general model of a disordered copolymer with adsorption. This includes, as particular cases, a generalization of the copolymer at a selective interface introduced by Garel et al. [Europhys. Lett. 8 (1989) 9–13], pinning and wetting models in various dimensions, and the Poland–Scheraga model of DNA denaturation. We prove a new variational upper bound for the free energy via an estimation of noninteger moments of the partition function. As an application, we show that for strong disorder the quenched critical point differs from the annealed one, for example, if the disorder distribution is Gaussian. In particular, for pinning models with loop exponent 0<α<1/2 this implies the existence of a transition from weak to strong disorder. For the copolymer model, under a (restrictive) condition on the law of the underlying renewal, we show that the critical point coincides with the one predicted via renormalization group arguments in the theoretical physics literature. A stronger result holds for a “reduced wetting model” introduced by Bodineau and Giacomin [J. Statist. Phys. 117 (2004) 801–818]: without restrictions on the law of the underlying renewal, the critical point coincides with the corresponding renormalization group prediction.

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Ann. Appl. Probab., Volume 18, Number 4 (2008), 1569-1587.

First available in Project Euclid: 21 July 2008

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Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.) 60K05: Renewal theory

Pinning and wetting models copolymers at selective interfaces annealed bounds fractional moments


Toninelli, Fabio Lucio. Disordered pinning models and copolymers: Beyond annealed bounds. Ann. Appl. Probab. 18 (2008), no. 4, 1569--1587. doi:10.1214/07-AAP496.

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