19 research outputs found
Large deviations of the empirical current for the boundary driven Kawasaki process with long range interaction
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
Metastable Markov chains: from the convergence of the trace to the convergence of the finite-dimensional distributions
We consider continuous-time Markov chains which display a family of wells at
the same depth. We provide sufficient conditions which entail the convergence
of the finite-dimensional distributions of the order parameter to the ones of a
finite state Markov chain. We also show that the state of the process can be
represented as a time-dependent convex combination of metastable states, each
of which is supported on one well
Hydrostatics and dynamical large deviations of boundary driven gradient symmetric exclusion
We prove hydrostatics of boundary driven gradient exclusion processes, Fick's
law and we present a simple proof of the dynamical large deviations principle
which holds in any dimensionComment: 30 page
Boundary driven Kawasaki process with long range interaction: dynamical large deviations and steady states
A particle system with a single locally-conserved field (density) in a
bounded interval with different densities maintained at the two endpoints of
the interval is under study here. The particles interact in the bulk through a
long range potential parametrized by and evolve according to an
exclusion rule. It is shown that the empirical particle density under the
diffusive scaling solves a quasi-linear integro-differential evolution equation
with Dirichlet boundary conditions. The associated dynamical large deviation
principle is proved. Furthermore, for small enough, it is also
demonstrated that the empirical particle density obeys a law of large numbers
with respect to the stationary measures (hydrostatic). The macroscopic particle
density solves a non local, stationary, transport equation
A boundary driven generalised contact process with exchange of particles: Hydrodynamics in infinite volume
International audienceWe consider a two species process which evolves in a finite or infinite domain in contact with particles reservoirs at different densities, according to the superposition of a generalised contact process and a rapid-stirring dynamics in the bulk of the domain, and a creation/annihilation mechanism at its boundaries. For this process, we study the law of large numbers for densities and current. The limiting equations are given by a system of non-linear reaction-diffusion equations with Dirichlet boundary conditions
Hydrodynamic and hydrostatic limit for a generalized contact process with mixed boundary conditions
We consider an interacting particle system which models the sterile insect
technique. It is the superposition of a generalized contact process with
exchanges of particles on a finite cylinder with open boundaries (see Kuoch et
al., 2017). We show that when the system is in contact with reservoirs at
different slowdown rates, the hydrodynamic limit is a set of coupled non linear
reaction-diffusion equations with mixed boundary conditions. We also prove the
hydrostatic limit when the macroscopic equations exhibit a unique attractor
Quenched large deviations for Glauber evolution with Kac interaction and Random Field
We study a spin-flip model with Kac type interaction, in the presence of a
random field given by i.i.d. bounded random variables. The system, spatially
inhomogeneous, evolves according to a non conservative (Glauber) dynamics. We
show an almost sure (with respect to the random field) large deviations
principle for the empirical magnetizations of this process. The rate functional
depends on the statistical properties of the external random field, it is lower
semicontinuous with compact level sets.Comment: 40 page
Lattice gas model in random medium and open boundaries: hydrodynamic and relaxation to the steady state
We consider a lattice gas interacting by the exclusion rule in the presence
of a random field given by i.i.d. bounded random variables in a bounded domain
in contact with particles reservoir at different densities. We show, in
dimensions , that the rescaled empirical density field almost surely,
with respect to the random field, converges to the unique weak solution of a
non linear parabolic equation having the diffusion matrix determined by the
statistical properties of the external random field and boundary conditions
determined by the density of the reservoir. Further we show that the rescaled
empirical density field, in the stationary regime, almost surely with respect
to the random field, converges to the solution of the associated stationary
transport equation