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On the partition function of a directed polymer in a Gaussian random environment
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  • Published: November 2002

On the partition function of a directed polymer in a Gaussian random environment

  • Philippe Carmona1 &
  • Yueyun Hu2 

Probability Theory and Related Fields volume 124, pages 431–457 (2002)Cite this article

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  • 81 Citations

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Abstract.

 The purpose of this work is the study of the partition function of a -dimensional lattice directed polymer in a Gaussian random environment being the inverse of temperature). In the low-dimensional cases , we prove that for all , the renormalized partition function converges to 0 and the correlation of two independent configurations does not converge to 0. In the high dimensional case (), a lower tail of has been obtained for small . Furthermore, we express some thermodynamic quantities in terms of the path measure alone.

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Authors and Affiliations

  1. Laboratoire de Statistique et Probabilités, Université Paul Sabatier, 118, route de Narbonne, F-31062 Toulouse cedex 04, France. e-mail: carmona@cict.fr, , , , , , FR

    Philippe Carmona

  2. Laboratoire de Probabilités et Modèles Aléatoires (CNRS UMR-7599), Université Paris VI, 4 Place Jussieu, F-75252 Paris cedex 05, France. e-mail: hu@ccr.jussieu.fr, , , , , , FR

    Yueyun Hu

Authors
  1. Philippe Carmona
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  2. Yueyun Hu
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Additional information

Received: 8 June 2001 / Revised version: 8 February 2002 / Published online: 22 August 2002

Mathematics Subject Classification (2000): 60K37, 82D30

Key words or phrases: Directed polymer in random environment – Gaussian environment – partition function

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Carmona, P., Hu, Y. On the partition function of a directed polymer in a Gaussian random environment. Probab Theory Relat Fields 124, 431–457 (2002). https://doi.org/10.1007/s004400200213

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  • Issue Date: November 2002

  • DOI: https://doi.org/10.1007/s004400200213

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Keywords

  • Polymer
  • Partition Function
  • Random Environment
  • Directed Polymer
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