Proof of the Razumov-Stroganov conjecture for some infinite families of link patterns.
Propagation of chaos for the 2D viscous vortex model
We consider a stochastic system of particles, usually called vortices in that setting, approximating the 2D Navier-Stokes equation written in vorticity. Assuming that the initial distribution of the position and circulation of the vortices has finite (partial) entropy and a finite moment of positive order, we show that the empirical measure of the particle system converges in law to the unique (under suitable a priori estimates) solution of the 2D Navier-Stokes equation. We actually prove a slightly...
Properties of operators related to the Boltzmann collision term
Properties of the solution map for a first order linear problem.
Propriétés dispersives pour des équations cinétiques et applications à l’équation de Vlasov-Poisson
On considère l’équation de Vlasov-Poisson en dimension 3. On montre des résultats d’existence et d’unicité de solutions faibles de l’équation de Vlasov-Poisson avec densité bornée pour des données initiales ayant strictement moins de six moments dans . La preuve est basée sur une nouvelle approche qui consiste à établir des effets de moments a priori pour des équations de transport avec des termes de force peu réguliers.
Propriétés ergodiques, en mesure infinie, de certains systèmes dynamiques fibrés
Qualitative investigation of the three-phase solutions of the sine-Laplace equation
Qualitative properties of a certain kinetic model of a binary gas.
Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach.
We present here a simplified version of recent results obtained with B. Helffer and M. Klein. They are concerned with the exponentally small eigenvalues of the Witten Laplacian on -forms. We show how the Witten complex structure is better taken into account by working with singular values. This provides a convenient framework to derive accurate approximations of the first eigenvalues of and solves efficiently the question of weakly resonant wells.
Quantitative concentration inequalities on sample path space for mean field interaction
We consider the approximation of a mean field stochastic process by a large interacting particle system. We derive non-asymptotic large deviation bounds measuring the concentration of the empirical measure of the paths of the particles around the law of the process. The method is based on a coupling argument, strong integrability estimates on the paths in Hölder norm, and a general concentration result for the empirical measure of identically distributed independent paths.
Quantum curve in -oscillator model.
Quantum detailed balance
Quantum detailed balance conditions with time reversal: the finite-dimensional case
We classify generators of quantum Markov semigroups on (h), with h finite-dimensional and with a faithful normal invariant state ρ satisfying the standard quantum detailed balance condition with an anti-unitary time reversal θ commuting with ρ, namely for all x,y ∈ and t ≥ 0. Our results also show that it is possible to find a standard form for the operators in the Lindblad representation of the generators extending the standard form of generators of quantum Markov semigroups satisfying the usual...
Quantum dynamical systems with quasi-discrete spectrum.
Quantum Dynamics and generalized fractal dimensions: an introduction
We review some recent results on quantum motion analysis, and in particular lower bounds for moments in quantum dynamics. The goal of the present exposition is to stress the role played by quantities we shall call Transport Integrals and by the so called generalized dimensions of the spectral measure in the analysis of quantum motion. We start with very simple derivations that illustrate how these quantities naturally enter the game. Then, gradually, we present successive improvements, up to most...
Quantum Euler-Poisson systems: Existence of stationary states
A one-dimensional quantum Euler-Poisson system for semiconductors for the electron density and the electrostatic potential in bounded intervals is considered. The existence and uniqueness of strong solutions with positive electron density is shown for quite general (possibly non-convex or non-monotone) pressure-density functions under a “subsonic” condition, i.e. assuming sufficiently small current densities. The proof is based on a reformulation of the dispersive third-order equation for the electron...
Quantum graph spectra of a graphyne structure
We study the dispersion relations and spectra of invariant Schrödinger operators on a graphyne structure (lithographite). In particular, description of different parts of the spectrum, band-gap structure, and Dirac points are provided.
Quantum information from graviton-matter gas.
Quantum integrable 1D anyonic models: construction through braided Yang-Baxter equation.
Quantum integrable model of an arrangement of hyperplanes.