N
Nicolas Fournier
Researcher at University of Paris
Publications - 110
Citations - 3438
Nicolas Fournier is an academic researcher from University of Paris. The author has contributed to research in topics: Boltzmann equation & Stochastic differential equation. The author has an hindex of 29, co-authored 106 publications receiving 3044 citations. Previous affiliations of Nicolas Fournier include Nancy-Université & Institut Élie Cartan de Lorraine.
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On the rate of convergence in Wasserstein distance of the empirical measure
Nicolas Fournier,Arnaud Guillin +1 more
TL;DR: In this article, the authors studied the convergence rate of the Wasserstein distance of a sample of a given probability distribution with respect to the probability distribution of a random sample, and provided a non-asymptotic bound on the convergence of the sample to a stationary Markov chain.
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On the rate of convergence in Wasserstein distance of the empirical measure
Nicolas Fournier,Arnaud Guillin +1 more
TL;DR: In this paper, the authors consider the convergence of a probability distribution to a given probability distribution in the Wasserstein distance of order $p>0, and provide some satisfying non-asymptotic $L^p$-bounds and concentration inequalities, for any values of $p > 0 and $d\geq 1.
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Existence of Self-Similar Solutions to Smoluchowski’s Coagulation Equation
TL;DR: The existence of self-similar solutions to Smoluchowski's coagulation equation has been conjectured for several years by physicists, and numerical simulations have confirmed the validity of this conjecture as mentioned in this paper.
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Hawkes processes on large networks
TL;DR: In this paper, the authors generalize the construction of multivariate Hawkes processes to a possibly infinite network of counting processes on a directed graph G. The process is constructed as the solution to a system of Poisson driven stochastic differential equations, for which they prove pathwise existence and uniqueness under some reasonable conditions.
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Propagation of chaos for the 2D viscous vortex model
TL;DR: In this article, the authors consider a stochastic system of vortices and show that the empirical measure of the particle system converges in law to the unique (under suitable a priori estimates) solution of the 2D Navier-Stokes equation.