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Renewal convergence rates and correlation decay for homogeneous pinning models
- Source :
- Electron. J. Probab. 13 (2008), 513-529, Electronic Journal of Probability, Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2008, 13 (18), pp.513-529, Electronic Journal of Probability, 2008, 13 (18), pp.513-529
- Publication Year :
- 2007
- Publisher :
- arXiv, 2007.
-
Abstract
- A class of discrete renewal processes with super-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.<br />Comment: 13 pages
- Subjects :
- Statistics and Probability
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]
Phase transition
Exponential Tails
MathematicsofComputing_GENERAL
FOS: Physical sciences
01 natural sciences
010104 statistics & probability
InformationSystems_GENERAL
Decay of Correlations
Exponential growth
60K05
Convergence (routing)
FOS: Mathematics
Limit (mathematics)
Renewal theory
0101 mathematics
GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries)
Mathematical Physics
ComputingMilieux_MISCELLANEOUS
Mathematics
Renewal Theory
Criticality
Speed of Convergence to Equilibrium
010102 general mathematics
Mathematical analysis
Probability (math.PR)
Statistical mechanics
Mathematical Physics (math-ph)
60K35
82B27
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
Distribution (mathematics)
Rate of convergence
Pinning Models
Statistics, Probability and Uncertainty
Mathematics - Probability
Subjects
Details
- ISSN :
- 10836489
- Database :
- OpenAIRE
- Journal :
- Electron. J. Probab. 13 (2008), 513-529, Electronic Journal of Probability, Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2008, 13 (18), pp.513-529, Electronic Journal of Probability, 2008, 13 (18), pp.513-529
- Accession number :
- edsair.doi.dedup.....b3333dcb65a492f1d3bfe8050878533f
- Full Text :
- https://doi.org/10.48550/arxiv.0706.0341