467 citations · 815 across the 13 of their papers we have counts for
14 papers
On the kinetic Fokker--Planck equation in curved geometry
Cédric Villani
These notes are devoted to the kinetic Fokker--Planck equation on the tangent bundle of a compact Riemannian manifold, with motivations coming from relativistic kinetic theory of g…
Lyapunov functionals for boundary-driven nonlinear drift-diffusions
T. Bodineau, J. L. Lebowitz, C. Mouhot +1
We exhibit a large class of Lyapunov functionals for nonlinear drift-diffusion equations with non-homogeneous Dirichlet boundary conditions. These are generalizations of large devi…
A curved Brunn--Minkowski inequality on the discrete hypercube
Yann Ollivier, Cédric Villani
We compare two approaches to Ricci curvature on non-smooth spaces, in the case of the discrete hypercube . While the coarse Ricci curvature of the first author readily y…
Celebrating Cercignani's conjecture for the Boltzmann equation
Laurent Desvillettes, Clément Mouhot, Cédric Villani
Cercignani's conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann's nonlinear integral operator in rarefied gas dynamics. Rel…
Spectral methods for the non cut-off Boltzmann equation and numerical grazing collision limit
Lorenzo Pareschi, Giuseppe Toscani, Cédric Villani
In this paper we study the numerical passage from the spatially homogeneous Boltzmann equation without cut-off to the Fokker-Planck-Landau equation in the so-called grazing collisi…
On Landau damping
Clément Mouhot, Cédric Villani
Going beyond the linearized study has been a longstanding problem in the theory of Landau damping. In this paper we establish exponential Landau damping in analytic regularity. The…