38 citations · 134 across the 17 of their papers we have counts for
20 papers
Quantitative Stability of Barycenters in the Wasserstein Space
Guillaume Carlier, Alex Delalande, Quentin Merigot
Wasserstein barycenters define averages of probability measures in a geometrically meaningful way. Their use is increasingly popular in applied fields, such as image, geometry or l…
Non-asymptotic convergence bounds for Wasserstein approximation using point clouds
Quentin Merigot, Filippo Santambrogio, Clément Sarrazin
Several issues in machine learning and inverse problems require to generate discrete data, as if sampled from a model probability distribution. A common way to do so relies on the…
Convergence of a Lagrangian discretization for barotropic fluids and porous media flow
Thomas Gallouët, Quentin Merigot, Andrea Natale
When expressed in Lagrangian variables, the equations of motion for compressible (barotropic) fluids have the structure of a classical Hamiltonian system in which the potential ene…
A Damped Newton Algorithm for Generated Jacobian Equations
Anatole Gallouët, Quentin Merigot, Boris Thibert
Generated Jacobian Equations have been introduced by Trudinger [Disc. cont. dyn. sys (2014), pp. 1663-1681] as a generalization of Monge-Amp{è}re equations arising in optimal trans…
Optimal transport: discretization and algorithms
Quentin Merigot, Boris Thibert
This chapter describes techniques for the numerical resolution of optimal transport problems. We will consider several discretizations of these problems, and we will put a strong f…
Quantitative stability of optimal transport maps and linearization of the 2-Wasserstein space
Quentin Mérigot, Alex Delalande, Frédéric Chazal
This work studies an explicit embedding of the set of probability measures into a Hilbert space, defined using optimal transport maps from a reference probability density. This emb…