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Processus d'exclusion asymétrique: Effet du désordre, Grandes déviations et fluctuations

Abstract : This thesis presents a series of works dealing with the open asymmetric exclusion process.

In a first part, we give numerical evidences showing that the position of the first order phase transition in the totally asymmetric exclusion process become sample-dependent when quenched, sitewise disorder is added to the jump rates. These numerical simulations are compared with analytic prediction based on a mean field approach.

In a second part, we study the macroscopic properties of the density profile in the stationary state of the exclusion process. We firstly derive the large deviation function for the weakly asymmetric exclusion process. Our expression is shown to link those of the large deviation function of the symmetric and the totally asymmetric exclusion process, which have been previously derived. Next, we compute the distribution of the small density fluctuations in the weakly and totally asymmetric process. These fluctuations can be written as the sum of two independent random functions. We show that in the maximal current phase of the totally asymmetric exclusion process, these fluctuations are non-gaussien. From the fluctuation distribution, we derive the density correlation functions in the stationary state.
Our derivations of the density profile properties are based on a rewriting of the probability of a given profile as a sum over abstract paths. In order to generalize such an expression, a microscopic dynamic on those paths is constructed.
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Contributor : Camille Enaud <>
Submitted on : Thursday, November 10, 2005 - 9:24:22 PM
Last modification on : Thursday, December 10, 2020 - 12:37:24 PM
Long-term archiving on: : Friday, September 14, 2012 - 3:50:19 PM


  • HAL Id : tel-00010955, version 1


Camille Enaud. Processus d'exclusion asymétrique: Effet du désordre, Grandes déviations et fluctuations. Analyse de données, Statistiques et Probabilités []. Université Pierre et Marie Curie - Paris VI, 2005. Français. ⟨tel-00010955⟩



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