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Sharp critical behavior for pinning model in random correlated environment

Berger, Quentin; Lacoin, Hubert (2012), Sharp critical behavior for pinning model in random correlated environment, Stochastic Processes and their Applications, 122, 4, p. 1397-1436. http://dx.doi.org/10.1016/j.spa.2011.12.007

Type
Article accepté pour publication ou publié
External document link
http://fr.arXiv.org/abs/1104.4969
Date
2012
Journal name
Stochastic Processes and their Applications
Volume
122
Number
4
Publisher
Elsevier
Pages
1397-1436
Publication identifier
http://dx.doi.org/10.1016/j.spa.2011.12.007
Metadata
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Author(s)
Berger, Quentin cc
Lacoin, Hubert
Abstract (EN)
This article investigates the effect for random pinning models of long range power-law decaying correlations in the environment. For a particular type of environment based on a renewal construction, we are able to sharply describe the phase transition from the delocalized phase to the localized one, giving the critical exponent for the (quenched) free-energy, and proving that at the critical point the trajectories are fully delocalized. These results contrast with what happens both for the pure model (i.e. without disorder) and for the widely studied case of i.i.d. disorder, where the relevance or irrelevance of disorder on the critical properties is decided via the so-called Harris Criterion.
Subjects / Keywords
correlation; path behavior; Polymer pinning; quenched disorder; free energy

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