Second class particles in the rarefaction fan
Selfgravitating systems in Newtonian theory - the Vlasov-Poisson system
We give a review of results on the initial value problem for the Vlasov--Poisson system, concentrating on the main ingredients in the proof of global existence of classical solutions.
Semiclassical, asymptotics and dispersive effects for Hartree-Fock systems
Shape transition under excess self-intersections for transient random walk
We reveal a shape transition for a transient simple random walk forced to realize an excess q-norm of the local times, as the parameter q crosses the value qc(d)=d/(d−2). Also, as an application of our approach, we establish a central limit theorem for the q-norm of the local times in dimension 4 or more.
Simulating Kinetic Processes in Time and Space on a Lattice
We have developed a chemical kinetics simulation that can be used as both an educational and research tool. The simulator is designed as an accessible, open-source project that can be run on a laptop with a student-friendly interface. The application can potentially be scaled to run in parallel for large simulations. The simulation has been successfully used in a classroom setting for teaching basic electrochemical properties. We have shown that...
Some results for poisoning in a catalytic model.
Steady states for a fragmentation equation with size diffusion
The existence of a one-parameter family of stationary solutions to a fragmentation equation with size diffusion is established. The proof combines a fixed point argument and compactness techniques.
Stochastic dynamics macroscopically governed by the porous medium equation for isothermal flow.
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
Un modèle du votant en milieu aléatoire
Un teorema de mecánica estadística relativista y los espacios de Hilbert-Lobatschewsky.
Se expone la geometría diferencial del espacio de las velocidades relativistas y se obtiene la función de distribución de velocidades de un gas de partículas relativistas, que modifica la función de Maxwell de Mecánica Estadística Clásica. Se introducen los espacios de Hilbert-Lobatschewsky.
Uniqueness of invariant product measures for elliptic infinite dimensional diffusions and particle spin systems
Consider an infinite dimensional diffusion process process on , where is the circle, defined by the action of its generator on local functions as . Assume that the coefficients, and are smooth, bounded, finite range with uniformly bounded second order partial derivatives, that is only a function of and that . Suppose is an invariant product measure. Then, if is the Lebesgue measure or if , it is the unique invariant measure. Furthermore, if is translation invariant, then...