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Hierarchical pinning model with site disorder: disorder is marginally relevant
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  • Published: 19 May 2009

Hierarchical pinning model with site disorder: disorder is marginally relevant

  • Hubert Lacoin1 

Probability Theory and Related Fields volume 148, pages 159–175 (2010)Cite this article

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  • 14 Citations

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Abstract

We study a hierarchical disordered pinning model with site disorder for which, like in the bond disordered case (Derrida et al. in J Stat Phys 66:1189–1213, 1992 and Giacomin et al. in Probab. Theor. Rel. Fields 2009, arXiv:0711.4649 [math.PR]), there exists a value of a parameter b (which enters in the definition of the hierarchical lattice) that separates an irrelevant disorder regime and a relevant disorder regime. We show that for such a value of b the critical point of the disordered system is different from the critical point of the annealed version of the model. The proof goes beyond the technique used in Giacomin et al. (Probab. Theor. Rel. Fields 2009, arXiv:0711.4649 [math.PR]) and it takes explicitly advantage of the inhomogeneous character of the Green function of the model.

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Authors and Affiliations

  1. Laboratoire de Probabilités et Modèles Aléatoires, Université Paris Diderot (CNRS U.M.R. 7599), U.F.R. Mathématiques, Case 7012 (Site Chevaleret), 75205, Paris Cedex 13, France

    Hubert Lacoin

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  1. Hubert Lacoin
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Correspondence to Hubert Lacoin.

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Cite this article

Lacoin, H. Hierarchical pinning model with site disorder: disorder is marginally relevant. Probab. Theory Relat. Fields 148, 159–175 (2010). https://doi.org/10.1007/s00440-009-0226-6

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  • Received: 19 September 2008

  • Revised: 23 April 2009

  • Published: 19 May 2009

  • Issue Date: September 2010

  • DOI: https://doi.org/10.1007/s00440-009-0226-6

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Keywords

  • Hierarchical pinning models
  • Diamond lattices
  • Quenched disorder
  • Critical behavior

Mathematics Subject Classification (2000)

  • 60K37
  • 82B44
  • 37H99
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