52 citations · 272 across the 26 of their papers we have counts for
8 papers · 1 filter
Intermediate model between Majority voter PCA and its Mean Field model
Jean Bricmont, Hanne Van Den Bosch
Probabilistic Cellular Automata (PCA) are simple models used to study dynamical phase transitions. There exist mean field approximations to PCA that can be shown to exhibit a phase…
Diffusion in Energy Conserving Coupled Maps
Jean Bricmont, Antti Kupiainen
We consider a dynamical system consisting of subsystems indexed by a lattice. Each subsystem has one conserved degree of freedom ("energy") the rest being uniformly hyperbolic. The…
Random walks in space time mixing environments
Jean Bricmont, Antti Kupiainen
We prove that random walks in random environments, that are exponentially mixing in space and time, are almost surely diffusive, in the sense that their scaling limit is given by t…
Approach to equilibrium for the phonon Boltzmann equation
Jean Bricmont, Antti Kupiainen
We study the asymptotics of solutions of the Boltzmann equation describing the kinetic limit of a lattice of classical interacting anharmonic oscillators. We prove that, if the ini…
Fourier's Law from Closure Equations
Jean Bricmont, Antti Kupiainen
We give a rigorous derivation of Fourier's law from a system of closure equations for a nonequilibrium stationary state of a Hamiltonian system of coupled oscillators subjected to…
On the derivation of Fourier's law for coupled anharmonic oscillators
Jean Bricmont, Antti Kupiainen
We study the Hamiltonian system made of weakly coupled anharmonic oscillators arranged on a three dimensional lattice and subjected to a stochastic forcing mimicking heat baths of…
Renormalization Group and the Melnikov Problem for PDE's
Jean Bricmont, Antti Kupiainen, Alain Schenkel
We give a new proof of persistence of quasi-periodic, low dimensional elliptic tori in infinite dimensional systems. The proof is based on a renormalization group iteration that wa…
Exponential Mixing of the 2D Stochastic Navier-Stokes Dynamics
J. Bricmont, A. Kupiainen, R. Lefevere
We consider the Navier-Stokes equation on a two dimensional torus with a random force which is white noise in time, and excites only a finite number of modes. The number of excited…