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2008 Renewal convergence rates and correlation decay for homogeneous pinning models
Giambattista Giacomin
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Electron. J. Probab. 13: 513-529 (2008). DOI: 10.1214/EJP.v13-497


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.


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Giambattista Giacomin. "Renewal convergence rates and correlation decay for homogeneous pinning models." Electron. J. Probab. 13 513 - 529, 2008.


Accepted: 1 April 2008; Published: 2008
First available in Project Euclid: 1 June 2016

zbMATH: 1190.60086
MathSciNet: MR2386741
Digital Object Identifier: 10.1214/EJP.v13-497

Primary: 60K05
Secondary: 60K35 , 82B27

Keywords: Criticality , decay of correlations , exponential tails , Pinning models , renewal theory , speed of convergence to equilibrium

Vol.13 • 2008
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