# Hierarchical pinning model in correlated random environment

Quentin Berger; Fabio Lucio Toninelli

Annales de l'I.H.P. Probabilités et statistiques (2013)

- Volume: 49, Issue: 3, page 781-816
- ISSN: 0246-0203

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topBerger, Quentin, and Toninelli, Fabio Lucio. "Hierarchical pinning model in correlated random environment." Annales de l'I.H.P. Probabilités et statistiques 49.3 (2013): 781-816. <http://eudml.org/doc/272100>.

@article{Berger2013,

abstract = {We consider the hierarchical disordered pinning model studied in (J. Statist. Phys.66 (1992) 1189–1213), which exhibits a localization/delocalization phase transition. In the case where the disorder is i.i.d. (independent and identically distributed), the question of relevance/irrelevance of disorder (i.e. whether disorder changes or not the critical properties with respect to the homogeneous case) is by now mathematically rather well understood (Probab. Theory Related Fields148 (2010) 159–175, Pure Appl. Math.63 (2010) 233–265). Here we consider the case where randomness is spatially correlated and correlations respect the hierarchical structure of the model; in the non-hierarchical model our choice would correspond to a power-law decay of correlations. In terms of the critical exponent of the homogeneous model and of the correlation decay exponent, we identify three regions. In the first one (non-summable correlations) the phase transition disappears. In the second one (correlations decaying fast enough) the system behaves essentially like in the i.i.d. setting and the relevance/irrelevance criterion is not modified. Finally, there is a region where the presence of correlations changes the critical properties of the annealed system.},

author = {Berger, Quentin, Toninelli, Fabio Lucio},

journal = {Annales de l'I.H.P. Probabilités et statistiques},

keywords = {pinning models; polymer; disordered models; Harris criterion; critical phenomena; correlation; hierarchical models},

language = {eng},

number = {3},

pages = {781-816},

publisher = {Gauthier-Villars},

title = {Hierarchical pinning model in correlated random environment},

url = {http://eudml.org/doc/272100},

volume = {49},

year = {2013},

}

TY - JOUR

AU - Berger, Quentin

AU - Toninelli, Fabio Lucio

TI - Hierarchical pinning model in correlated random environment

JO - Annales de l'I.H.P. Probabilités et statistiques

PY - 2013

PB - Gauthier-Villars

VL - 49

IS - 3

SP - 781

EP - 816

AB - We consider the hierarchical disordered pinning model studied in (J. Statist. Phys.66 (1992) 1189–1213), which exhibits a localization/delocalization phase transition. In the case where the disorder is i.i.d. (independent and identically distributed), the question of relevance/irrelevance of disorder (i.e. whether disorder changes or not the critical properties with respect to the homogeneous case) is by now mathematically rather well understood (Probab. Theory Related Fields148 (2010) 159–175, Pure Appl. Math.63 (2010) 233–265). Here we consider the case where randomness is spatially correlated and correlations respect the hierarchical structure of the model; in the non-hierarchical model our choice would correspond to a power-law decay of correlations. In terms of the critical exponent of the homogeneous model and of the correlation decay exponent, we identify three regions. In the first one (non-summable correlations) the phase transition disappears. In the second one (correlations decaying fast enough) the system behaves essentially like in the i.i.d. setting and the relevance/irrelevance criterion is not modified. Finally, there is a region where the presence of correlations changes the critical properties of the annealed system.

LA - eng

KW - pinning models; polymer; disordered models; Harris criterion; critical phenomena; correlation; hierarchical models

UR - http://eudml.org/doc/272100

ER -

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