Large deviations of the empirical current for the boundary driven Kawasaki process with long range interaction

Mustapha Mourragui (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

We consider a lattice gas evolving in a bounded cylinder of length 2N + 1 and interacting via a Neuman Kac interaction of range N, in contact with particles reservoirs at different densities. We investigate the associated law of large numbers and large deviations of the empirical current and of the density. The hydrodynamic limit for the empirical density, obtained in the diffusive scaling, is given by a nonlocal, nonlinear evolution equation with Dirichlet boundary conditions.

Mots clés: Kawasaki process; Neuman Kac potential; Empirical current; Empirical density; Large deviations; Stationary nonequilibrium states; "Kawasaki process"; "Neuman Kac potential"; "Empirical current"; "Empirical density"; "Large deviations"; "Stationary nonequilibrium states".

Domaines: Probabilités [math.PR]

Mustapha Mourragui. Large deviations of the empirical current for the boundary driven Kawasaki process with long range interaction. 2014. ⟨hal-01002002v1⟩