The asymmetric simple exclusion model with multiple shocks
The integrated density of states for an interacting multiparticle homogeneous model and applications to the Anderson model.
The logarithmic Sobolev constant of Kawasaki dynamics under a mixing condition revisited
The mean-field limit for the dynamics of large particle systems
This short course explains how the usual mean-field evolution PDEs in Statistical Physics - such as the Vlasov-Poisson, Schrödinger-Poisson or time-dependent Hartree-Fock equations - are rigorously derived from first principles, i.e. from the fundamental microscopic models that govern the evolution of large, interacting particle systems.
The spectral gap for a Glauber-type dynamics in a continuous gas
The time for a critical nearest particle system to reach equilibrium starting with a large gap.
Tightness of voter model interfaces.
Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck equation
We consider a Vlasov-Fokker-Planck equation governing the evolution of the density of interacting and diffusive matter in the space of positions and velocities. We use a probabilistic interpretation to obtain convergence towards equilibrium in Wasserstein distance with an explicit exponential rate. We also prove a propagation of chaos property for an associated particle system, and give rates on the approximation of the solution by the particle system. Finally, a transportation inequality...
Two scales hydrodynamic limit for a model of malignant tumor cells