4 papers
Asymptotics of a two-species particle system associated to the doubly parabolic Keller-Segel equation in the plane
Nicolas Fournier, Milica TomaÅ¡eviÄ
We consider the two-species particle system introduced by Stevens (2000) related to the doubly parabolic Keller-Segel equation. It consists of cells and of a varying number of…
Mean-field theory via dissociated arrays for particle systems interacting through noisy weights
Nicolas Fournier, Datong Zhou
We study a mean-field limit for a -particle system in which each particle follows a diffusion and interacts with other particles through a weight on each directed edge. Each wei…
Markov decision processes: on the convergence of the Monte-Carlo first visit algorithm
Sylvain Delattre, Nicolas Fournier
We consider the Monte-Carlo first visit algorithm, of which the goal is to find the optimal control in a Markov decision process with finite state space and finite number of possib…
Monge-Kantorovich distance for PDEs: the coupling method
Nicolas Fournier, Benoît Perthame
We informally review a few PDEs for which the Monge-Kantorovich distance between pairs of solutions, possibly with some judicious cost function, decays: heat equation, Fokker-Planc…