Open Access
September 2009 On the irrelevant disorder regime of pinning models
Giambattista Giacomin, Fabio Lucio Toninelli
Ann. Probab. 37(5): 1841-1875 (September 2009). DOI: 10.1214/09-AOP454


Recent results have lead to substantial progress in understanding the role of disorder in the (de)localization transition of polymer pinning models. Notably, there is an understanding of the crucial issue of disorder relevance and irrelevance that is now rigorous. In this work, we exploit interpolation and replica coupling methods to obtain sharper results on the irrelevant disorder regime of pinning models. In particular, in this regime, we compute the first order term in the expansion of the free energy close to criticality and this term coincides with the first order of the formal expansion obtained by field theory methods. We also show that the quenched and quenched averaged correlation length exponents coincide, while, in general, they are expected to be different. Interpolation and replica coupling methods in this class of models naturally lead to studying the behavior of the intersection of certain renewal sequences and one of the main tools in this work is precisely renewal theory and the study of these intersection renewals.


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Giambattista Giacomin. Fabio Lucio Toninelli. "On the irrelevant disorder regime of pinning models." Ann. Probab. 37 (5) 1841 - 1875, September 2009.


Published: September 2009
First available in Project Euclid: 21 September 2009

zbMATH: 1181.60148
MathSciNet: MR2561435
Digital Object Identifier: 10.1214/09-AOP454

Primary: 60K05 , 60K35 , 60K37 , 82B41 , 82B44

Keywords: Directed polymers , Harris criterion , intersection of renewals , irrelevant disorder , Pinning and wetting models , renewal theory

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 5 • September 2009
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