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Modèles de polymères dirigés en milieux aléatoires

Abstract : We study several models of directed polymers in random environments. For the classical model on Z^d, we study the convergence of the environments seen by the particle in the weak disorder region. We prove strong results for very high values of the temperature. We then give a complete treatment of the partition function of directed polymers on the diamond hierarchical lattice. Finally, we study the free energy of directed polymers in random environments on Z^d in very asymmetric boxes. We prove that, in a particular regime, it coincides with the free energy of a continuous time model in a Brownian environment. For d=1, the exact value of this free energy is known. We also study one-dimensional directed polymers with a huge drift. We give the exact value of the free energy and compute the order of fluctuations of the partition function.
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Contributor : Gregorio Moreno Flores <>
Submitted on : Saturday, June 5, 2010 - 7:40:00 PM
Last modification on : Wednesday, December 9, 2020 - 3:13:13 PM
Long-term archiving on: : Friday, September 17, 2010 - 12:28:02 PM


  • HAL Id : tel-00489557, version 1


Gregorio Moreno Flores. Modèles de polymères dirigés en milieux aléatoires. Mathématiques [math]. Université Paris-Diderot - Paris VII, 2010. Français. ⟨tel-00489557⟩



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