Se encontraron 2 investigaciones
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.
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  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  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  and  to extend the result in  to the nonreversible case.