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Last name: BERNARDIN
First name: Cédric
International audience
A fractional Fick's law and fractional hydrostatics for the one dimensional exclusion process with long jumps in contact with infinite reservoirs at different densities on the left and on the right are derived.
With respect to a class of long-range exclusion processes on Z d , with single particle transition rates of order | · | −(d+α) , starting under Bernoulli invariant measure ν ρ with density ρ, we consider the fluctuation behavior of occupation times at a vertex and more general additive functionals. Part of our motivation is to investigate the...
We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit. We prove that the distribution of these fluctuations converge to a gaussian space-time field that is delta correlated in time but with long-range correlations in space.
We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit. We prove that the distribution of these fluctuations converge to a gaussian space-time field that is delta correlated in time but with long-range correlations in space.
We consider a Hamiltonian lattice field model with two conserved quantities, energy and volume, perturbed by stochastic noise preserving the two previous quantities. It is known that this model displays anomalous diffusion of energy of fractional type due to the conservation of the volume [5, 3]. We superpose to this system a second stochastic...
In [2] it has been proved that a linear Hamiltonian lattice field perturbed by a conservative stochastic noise belongs to the 3/2-Lévy/Diffusive universality class in the nonlinear fluctuating theory terminology [15], i.e. energy superdiffuses like an asymmetric stable 3/2-Lévy process and volume like a Brownian motion. According to this theory...
We study the hydrodynamic limit for a model of symmetric exclusion processes with long jumps heavy-tailed and in contact with infinitely extended reservoirs. We show how the corresponding hydrodynamic equations are affected by the parameters defining the model. The hydrodynamic equations are characterized by a class of super-diffusive operators...
We study the hydrodynamic limit for a model of symmetric exclusion processes with long jumps heavy-tailed and in contact with infinitely extended reservoirs. We show how the corresponding hydrodynamic equations are affected by the parameters defining the model. The hydrodynamic equations are characterized by a class of super-diffusive operators...
We analyze strong noise limit of some stochastic differential equations. We focus on the particular case of Belavkin equations, arising from quantum measurements, where Bauer and Bernard pointed out an intriguing behavior. As the noise grows larger, the solutions exhibits locally a collapsing, that is to say converge to jump processes, very...
International audience
We study the Green-Kubo (GK) formula κ(ε,ξ) for the heat conductivity of an infinite chain of d-dimensional finite systems (cells) coupled by a smooth nearest neighbour potential εV. The uncoupled systems evolve according to Hamiltonian dynamics perturbed stochastically by an energy conserving noise of strength ξ. Noting that κ(ε,ξ) exists and...
We review recent rigorous mathematical results about the macroscopic behaviour of harmonic chains with the dynamics perturbed by a random exchange of velocities between nearest neighbor particles. The random exchange models the effects of nonlinearities of anharmonic chains and the resulting dynamics have similar macroscopic behaviour. In...