The grazing collisions asymptotics of the non cut-off Kac equation
The incipient infinite cluster in high-dimensional percolation.
The initial value problem for nonlinear Boltzmann equation
The integrated density of states for an interacting multiparticle homogeneous model and applications to the Anderson model.
The Ising transducer
The jammed phase of the Biham-Middleton-Levine traffic model.
The kinetic transport equation in the case of Compton scattering.
The large-scale limit of Dyson's hierarchical vector valued model at low temperatures. The non-gaussian case. Part I : limit theorem for the average spin
The large-scale limit of Dyson's hierarchical vector-valued model at low temperatures. The non-gaussian case. Part II : description of the large-scale limit
The law of large numbers for ballistic, multi-dimensional random walks on random lattices with correlated sites
The local relaxation flow approach to universality of the local statistics for random matrices
We present a generalization of the method of the local relaxation flow to establish the universality of local spectral statistics of a broad class of large random matrices. We show that the local distribution of the eigenvalues coincides with the local statistics of the corresponding Gaussian ensemble provided the distribution of the individual matrix element is smooth and the eigenvalues {xj}j=1N are close to their classical location {γj}j=1N determined by the limiting density of eigenvalues. Under...
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