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The present Project proposes the study of the large deviation regime in a class of interacting particle systems. More precisely, we consider processes which are the superposition of two dynamics: the symmetric simple exclusion process (Kawasaki) and a spin-flip process (Glauber). Inspired in the Freidlin and Wentzell theory, the main objective of this project is to stablish a large deviation principle for the stationary measure of such processes with rate function associated to the quasi-potential of the dynamical large deviation rate function.
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The zero range process is an interacting particle system in which many indistinguishable particles occupy sites on a lattice. Each lattice site may contain an integer number of particles and these particles hop between neighboring sites with a rate that depends on the number of particles at the site of departure. In this project we consider a zero range process on a finite (fixed) lattice and in which the rates decrease to a positive constant. Under some conditions on the velocity of convergence of the rates, a condensation phenomenon occurs: the stationary measure concentrates on configurations of particles in which all but a few number of particles occupy one single site. The site with maximal occupancy is called the condensate. It has been studied in [7] the asymptotic evolution of the condensate: Fix an initial configuration of N particles with the majority of them located at one site and observe the position X^N_t of the condensate at each time t. Then, as N goes to infinity, it is proved in [7] that the law of the path X^N converges to the law of a Markov chain on the set o sites. Such result has been obtained under the assumption of reversibility. The objective of this project is to use the recent results obtained in [4] and [6] to extend the result in [7] to the nonreversible case.
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