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On the irrelevant disorder regime of pinning models
- Source :
- Ann. Probab. 37, no. 5 (2009), 1841-1875
- Publication Year :
- 2009
- Publisher :
- The Institute of Mathematical Statistics, 2009.
-
Abstract
- 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.<br />Comment: Published in at http://dx.doi.org/10.1214/09-AOP454 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
- Subjects :
- Statistics and Probability
Work (thermodynamics)
60K35, 60K37, 60K05, 82B41, 82B44 (Primary)
82B44
82B41
Harris criterion
01 natural sciences
irrelevant disorder
Directed polymers
intersection of renewals
010104 statistics & probability
Intersection
Probability theory
60K05
FOS: Mathematics
Field theory (psychology)
Renewal theory
Statistical physics
0101 mathematics
renewal theory
Mathematics
Replica
010102 general mathematics
Probability (math.PR)
Term (time)
60K37
60K35
pinning and wetting models
Statistics, Probability and Uncertainty
Mathematics - Probability
Interpolation
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Ann. Probab. 37, no. 5 (2009), 1841-1875
- Accession number :
- edsair.doi.dedup.....98b631334fa589cdcaf6781d82ca88b7