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
TypeArticle accepté pour publication ou publié
External document linkhttp://fr.arXiv.org/abs/1104.4969
Journal nameStochastic Processes and their Applications
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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 / Keywordscorrelation; path behavior; Polymer pinning; quenched disorder; free energy
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Pinning on a defect line: characterization of marginal disorder relevance and sharp asymptotics for the critical point shift Berger, Quentin; Lacoin, Hubert (2018) Article accepté pour publication ou publié