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Random pinning model with finite range correlations : disorder relevant regime
- Source :
- Stochastic Processes and their Applications, Stochastic Processes and their Applications, Elsevier, 2012, 122 (10), pp.3560--3579. ⟨10.1016/j.spa.2012.06.007⟩
- Publication Year :
- 2012
- Publisher :
- HAL CCSD, 2012.
-
Abstract
- The purpose of this paper is to show how one can extend some results on disorder relevance obtained for the random pinning model with i.i.d disorder to the model with finite range correlated disorder. In a previous work, the annealed critical curve of the latter model was computed, and equality of quenched and annealed critical points, as well as exponents, was proved under some conditions on the return exponent of the interarrival times. Here we complete this work by looking at the disorder relevant regime, where annealed and quenched critical points differ. All these results show that the Harris criterion, which was proved to be correct in the i.i.d case, remains valid in our setup. We strongly use Markov renewal constructions that were introduced in the solving of the annealed model.
- Subjects :
- Statistics and Probability
Phase transition
Work (thermodynamics)
Harris criterion
Perron–Frobenius theory
critical curve
Finite range
01 natural sciences
disorder relevance
010104 statistics & probability
Modelling and Simulation
finite range correlations
FOS: Mathematics
Statistical physics
Markov renewal theory
0101 mathematics
Mathematics
Discrete mathematics
Markov chain
Applied Mathematics
Probability (math.PR)
010102 general mathematics
fractional moments
16. Peace & justice
Critical curve
Perron-Frobenius theory
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
Pinning
phase transition
Modeling and Simulation
Exponent
Mathematics - Probability
Subjects
Details
- Language :
- English
- ISSN :
- 03044149
- Database :
- OpenAIRE
- Journal :
- Stochastic Processes and their Applications, Stochastic Processes and their Applications, Elsevier, 2012, 122 (10), pp.3560--3579. ⟨10.1016/j.spa.2012.06.007⟩
- Accession number :
- edsair.doi.dedup.....a2a09ded889de4b8b0a7d92f5dec156e