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|All Authors / Contributors:||
Katalin Nagy; Jozsef Fritz; Stefano Olla; Université Paris-Dauphine,
|Notes:||Thèse soutenue en co-tutelle.|
|Description:||1 vol. (85 p.) ; 30 cm|
|Responsibility:||Katalin Nagy ; sous la dir.de Jozsef Fritz et Stefano Olla.|
This thesis concerns three different models of interacting particle systems. In the first part of the thesis we give an elementary proof of the central limit theorem for one dimensional symmetric random walk in random environment and we derive the hydrodynamic limit of the symmetric simple exclusion in random environment. In the second part we investigate a hyperbolic and non-attractive lattice-gas model. By means of the method of compensated compactness, logarithmic Sobolev inequalities and the Lax entropy inequality we prove existence and uniqueness of the hydrodynamic limit even in the regime of shocks. In the third part of the thesis we consider a system of harmonic oscillators with multiplicative noise. We show that the equilibrium fluctuations of the conserved fields (energy and deformation) at a diffusive scaling are described by a couple of generalized Ornstein-Uhlenbeck processes.