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Renewal convergence rates and correlation decay for homogeneous pinning models

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1.	Title	Title of document	Renewal convergence rates and correlation decay for homogeneous pinning models
2.	Creator	Author's name, affiliation, country	Giambattista Giacomin; University Paris 7 - D. Diderot
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Renewal Theory; Speed of Convergence to Equilibrium; Exponential Tails; Pinning Models; Decay of Correlations; Criticality
3.	Subject	Subject classification	60K05; 60K35; 82B27
4.	Description	Abstract	A class of discrete renewal processes with exponentially decaying inter-arrival distributions coincides with the infinite volume limit of general homogeneous pinning models in their localized phase. Pinning models are statistical mechanics systems to which a lot of attention has been devoted both for their relevance for applications and because they are solvable models exhibiting a non-trivial phase transition. The spatial decay of correlations in these systems is directly mapped to the speed of convergence to equilibrium for the associated renewal processes. We show that close to criticality, under general assumptions, the correlation decay rate, or the renewal convergence rate, coincides with the inter-arrival decay rate. We also show that, in general, this is false away from criticality. Under a stronger assumption on the inter-arrival distribution we establish a local limit theorem, capturing thus the sharp asymptotic behavior of correlations.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	ANR (France)
7.	Date	(YYYY-MM-DD)	2008-04-01
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/497
10.	Identifier	Digital Object Identifier	10.1214/EJP.v13-497
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 13
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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