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Strong Disorder for a Certain Class of Directed Polymers in a Random Environment

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We study a model of directed polymers in a random environment with a positive recurrent Markov chain, taking values in a countable space Σ. The random environment is a family (\(g(i,x), i \geq 1,x \in \Sigma\)) of independent and identically distributed real-valued variables. The asymptotic behaviour of the normalized partition function is characterized: when the common law of the g(·,·) is infinitely divisible and the Markov chain is exponentially recurrent we prove that the normalized partition function converges exponentially fast towards zero at all temperatures.

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Authors and Affiliations

  1. Laboratoire Jean Leray, UMR 6629, Université de Nantes, 92208, F-44322, Nantes Cedex 03, France

    Philippe Carmona

  2. Dipartimento di Fisica, Instituto Nazionale di Fisica Nucleare, Università di Roma “La Sapienza”, Sezione di Roma 1, Piazzale Aldo Moro 2, I-00185, Roma, Italy

    Francesco Guerra

  3. Département de Mathématiques, Institut Galilée (L.A.G.A. UMR 7539), Université Paris XIII, 99 Avenue J-B Clément, 93430, Villetaneuse, France

    Yueyun Hu

  4. Laboratoire de Statistique et Probabilités, Université Paul Sabatier, 118 route de Narbonne, F-31062, Toulouse cedex 04, France

    Olivier Mejane

Authors
  1. Philippe Carmona
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  2. Francesco Guerra
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  3. Yueyun Hu
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  4. Olivier Mejane
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Correspondence to Philippe Carmona.

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Carmona, P., Guerra, F., Hu, Y. et al. Strong Disorder for a Certain Class of Directed Polymers in a Random Environment. J Theor Probab 19, 134–151 (2006). https://doi.org/10.1007/s10959-006-0010-9

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  • DOI: https://doi.org/10.1007/s10959-006-0010-9

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