195 citations · 626 across the 21 of their papers we have counts for
23 papers
Regularity estimates for diffusion semigroups on weighted Sobolev spaces
Maxime Hauray, Yen V. Vuong
In this work, we consider a class of second order uniformly elliptic operators with smooth and bounded coefficients. We provide some estimates on the norm of the semigroup generate…
Central limit theorem for a spatial stochastic epidemic model with mean field interaction
Maxime Hauray, Etienne Pardoux, Yen V. Vuong
In this article, we study an interacting particle system in the context of epidemiology where the individuals (particles) are characterized by their position and infection state. W…
Well-posedness of a 2D gyrokinetic model with equal Debye length and Larmor radius
Pierre-Antoine Giorgi, Maxime Hauray
We study here a 2D gyrokinetic model obtained in [Bostan-Finot-Hauray,CRAS,2016], which naturally appears as the limit of a Vlasov-Poisson system with a very large external uniform…
Conditional propagation of chaos in a spatial stochastic epidemic model with common noise
Yen V. Vuong, Maxime Hauray, Etienne Pardoux
We study a stochastic spatial epidemic model where the individuals carry two features: a position and an infection state, interact and move in . In this Markovian model,…
Particle approximation of the BGK equation
Paolo Buttà, Maxime Hauray, Mario Pulvirenti
In this paper we prove the convergence of a suitable particle system towards the BGK model. More precisely, we consider an interacting stochastic particle system in which each part…
Rigorous derivation of Lindblad equations from quantum jumps processes in 1D
Christophe Gomez, Maxime Hauray
We are interested by the behaviour of a 1D single heavy particle, interacting with an environment made of very fast particles in a thermal state. Assuming that the interactions are…
Uniform contractivity in Wasserstein metric for the original 1D Kac's model
Maxime Hauray
We study here a very popular 1D jump model introduced by Kac: it consists of velocities encountering random binary collisions at which they randomly exchange energy. We show th…
Propagation of chaos for the Vlasov-Poisson-Fokker-Planck system in 1D
Maxime Hauray, Samir Salem
We consider a particle system in 1D, interacting via repulsive or attractive Coulomb forces. We prove the trajectorial propagation of molecular chaos towards a nonlinear SDE associ…
Mean-field limit for collective behavior models with sharp sensitivity regions
José A. Carrillo, Young-Pil Choi, Maxime Hauray +1
We rigorously show the mean-field limit for a large class of swarming individual based models with local sharp sensitivity regions. For instance, these models include nonlocal repu…
Propagation of chaos for the Landau equation with moderately soft potentials
Nicolas Fournier, Maxime Hauray
We consider the 3D Landau equation for moderately soft potentials ( with the usual notation) as well as a stochastic system of particles approximating it. We first…
Stability issues in the quasineutral limit of the one-dimensional Vlasov-Poisson equation
Daniel Han-Kwan, Maxime Hauray
This work is concerned with the quasineutral limit of the one-dimensional Vlasov-Poisson equation, for initial data close to stationary homogeneous profiles. Our objective is three…
On Liouville transport equation with a force field in
Maxime Hauray
We prove the existence and uniqueness of renormalized solutions of the Liouville equation for particles with a interaction potential in execpt at the origin. This im…
On Two-dimensional Hamiltonian Transport Equations with coefficients
Maxime Hauray
We consider two-dimensional autonomous divergence free vector-fields in $\Lde_{loc}$. Under a condition on direction of the flow and on the set of critical points, we prove the exi…
De coherence for a heavy particle interacting with a light one: new analysis and numerics
Riccardo Adami, Maxime Hauray, Claudia Negulescu
We study the dynamics of a quantum heavy particle undergoing a repulsive interaction with a light one. The main motivation is the detailed description of the loss of coherence indu…
Mean field limit for the one dimensional Vlasov-Poisson equation
Maxime Hauray
We consider systems of particles in dimension one, driven by pair Coulombian or gravitational interactions. When the number of particles goes to infinity in the so called mean…
A new proof of the uniqueness of the flow for ordinary differential equations with BV vector fields
Maxime Hauray, Claude Le Bris
We provide in this article a new proof of the uniqueness of the flow solution to ordinary differential equations with vector-fields that have divergence in (or in $…
The derivation of Swarming models: Mean-Field Limit and Wasserstein distances
J. A. Carrillo, Y. -P. Choi, M. Hauray
These notes are devoted to a summary on the mean-field limit of large ensembles of interacting particles with applications in swarming models. We first make a summary of the kineti…
Propagation of chaos for the 2D viscous vortex model
Nicolas Fournier, Maxime Hauray, Stéphane Mischler
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 initi…
On Kac's Chaos And Related Problems
Maxime Hauray, Stéphane Mischler
This paper is devoted to establish quantitative and qualitative estimates related to the notion of chaos as firstly formulated by M. Kac in his study of mean-field limit for system…
Particles approximations of Vlasov equations with singular forces : Propagation of chaos
Pierre-Emmanuel Jabin, Maxime Hauray
We obtain the mean field limit and the propagation of chaos for a system of particles interacting with a singular interaction force of the type , with in dimension $…
Well-Posedness of a Diffusive Gyrokinetic Model
Maxime Hauray, Anne Nouri
We study a finite Larmor radius model used to describe the ions distributions in the core of a toka-mak plasma, that consist in a gyro-kinetic transport equation, coupled with an e…
Derivation of a gyrokinetic model. Existence and uniqueness of specific stationary solutions
Philippe Ghendrih, Maxime Hauray, Anne Nouri
A finite Larmor radius approximation is derived from the classical Vlasov equation, in the limit of large (and uniform) external magnetic field. We also provide an heuristic deriva…
N particles approximation of the Vlasov equations with singular potential
Maxime Hauray, Jabin Pierre-Emmanuel
On demontre la convergence pour tout temps d'une approximation de l'equation de Vlasov par un systeme de particules sans regularisation du champ, ceci pour des potentiels singulier…