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July 2017 Universality for the pinning model in the weak coupling regime
Francesco Caravenna, Fabio Lucio Toninelli, Niccolò Torri
Ann. Probab. 45(4): 2154-2209 (July 2017). DOI: 10.1214/16-AOP1109

Abstract

We consider disordered pinning models, when the return time distribution of the underlying renewal process has a polynomial tail with exponent $\alpha\in(\frac{1}{2},1)$. This corresponds to a regime where disorder is known to be relevant, that is, to change the critical exponent of the localization transition and to induce a nontrivial shift of the critical point. We show that the free energy and critical curve have an explicit universal asymptotic behavior in the weak coupling regime, depending only on the tail of the return time distribution and not on finer details of the models. This is obtained comparing the partition functions with corresponding continuum quantities, through coarse-graining techniques.

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Francesco Caravenna. Fabio Lucio Toninelli. Niccolò Torri. "Universality for the pinning model in the weak coupling regime." Ann. Probab. 45 (4) 2154 - 2209, July 2017. https://doi.org/10.1214/16-AOP1109

Information

Received: 1 May 2015; Revised: 1 January 2016; Published: July 2017
First available in Project Euclid: 11 August 2017

zbMATH: 1376.82036
MathSciNet: MR3693960
Digital Object Identifier: 10.1214/16-AOP1109

Subjects:
Primary: 82B44
Secondary: 60K35, 82D60

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 4 • July 2017
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