285 citations · 682 across the 44 of their papers we have counts for
51 papers
Asymptotics of a two-species particle system associated to the doubly parabolic Keller-Segel equation in the plane
Nicolas Fournier, Milica Tomašević
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…
Particle approximation of the doubly parabolic Keller-Segel equation in the plane
Nicolas Fournier, Milica Tomasevic
In this work, we study a stochastic system of N particles associated with the parabolic-parabolic Keller-Segel system. This particle system is singular and non Markovian in that it…
Convergence of the empirical measure in expected Wasserstein distance: non asymptotic explicit bounds in
Nicolas Fournier
We provide some non asymptotic bounds, with explicit constants, that measure the rate of convergence, in expected Wasserstein distance, of the empirical measure associated to an i.…
A simple proof of non-explosion for measure solutions of the Keller-Segel equation
Nicolas Fournier, Yoan Tardy
We give a simple proof, relying on a {\it two-particles} moment computation, that there exists a global weak solution to the -dimensional parabolic-elliptic Keller-Segel equatio…