The logarithmic Sobolev constant of Kawasaki dynamics under a mixing condition revisited
The magnetization at high temperature for a p-spin interaction model with external field
This paper is devoted to a detailed and rigorous study of the magnetization at high temperature for a p-spin interaction model with external field, generalizing the Sherrington-Kirkpatrick model. In particular, we prove that (the mean of a spin with respect to the Gibbs measure) converges to an explicitly given random variable, and that ⟨σ₁⟩,...,⟨σₙ⟩ are asymptotically independent.
The Markovian hyperbolic triangulation
We construct and study the unique random tiling of the hyperbolic plane into ideal hyperbolic triangles (with the three corners located on the boundary) that is invariant (in law) with respect to Möbius transformations, and possesses a natural spatial Markov property that can be roughly described as the conditional independence of the two parts of the triangulation on the two sides of the edge of one of its triangles.
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 metastability threshold for modified bootstrap percolation in dimensions.
The multitrace matrix model of scalar field theory on fuzzy .
The non-linear macroscopic model of Relativistic Extended Thermodynamics of an ultra-relativistic gas
The model for an ultra-relativistic gas is here considered in the framework of Extended Thermodynamics. The closure, satisfying exactly the principles of relativity and of entropy, is obtained by following the approach «at a macroscopic level». Our results are compared with the ones of the kinetic approach.
The number of unbounded components in the Poisson Boolean model of continuum percolation in hyperbolic space.
The one dimensional annealed δ-Lyapounov exponent
The parabolic Anderson model in a dynamic random environment: Basic properties of the quenched Lyapunov exponent
In this paper we study the parabolic Anderson equation , , , where the -field and the -field are -valued, is the diffusion constant, and is the discrete Laplacian. The -field plays the role of adynamic random environmentthat drives the equation. The initial condition , , is taken to be non-negative and bounded. The solution of the parabolic Anderson equation describes the evolution of a field of particles performing independent simple random walks with binary branching: particles jump...
The parabolic-parabolic Keller-Segel equation
I present in this note recent results on the uniqueness and stability for the parabolic-parabolic Keller-Segel equation on the plane, obtained in collaboration with S. Mischler in [11].
The periodic unfolding method for a class of parabolic problems with imperfect interfaces
In this paper, we use the adapted periodic unfolding method to study the homogenization and corrector problems for the parabolic problem in a two-component composite with ε-periodic connected inclusions. The condition imposed on the interface is that the jump of the solution is proportional to the conormal derivative via a function of order εγ with γ ≤ −1. We give the homogenization results which include those obtained by Jose in [Rev. Roum. Math. Pures Appl. 54 (2009) 189–222]. We also get the...
The phase field equations and gradient flows of marginal functions.
The phase transition of the number-theoretical spin chain.
The posterior metric and the goodness of gibbsianness for transforms of Gibbs measures.
The pressure of the two dimensional Coulomb gas at low and intermediate temperatures
The principle of the largest terms and quantum large deviations
We give an approach to large deviation type asymptotic problems without evident probabilistic representation behind. An example provided by the mean field models of quantum statistical mechanics is considered.
The probability of the triangle inequality in probabilistic metric squares.
The quasineutral limit problem in semiconductors sciences
The mathematical analysis on various mathematical models arisen in semiconductor science has attracted a lot of attention in both applied mathematics and semiconductor physics. It is important to understand the relations between the various models which are different kind of nonlinear system of P.D.Es. The emphasis of this paper is on the relation between the drift-diffusion model and the diffusion equation. This is given by a quasineutral limit from the DD model to the diffusion equation.
The rate of convergence for spectra of GUE and LUE matrix ensembles
We obtain optimal bounds of order O(n −1) for the rate of convergence to the semicircle law and to the Marchenko-Pastur law for the expected spectral distribution functions of random matrices from the GUE and LUE, respectively.