33 citations · 58 across the 8 of their papers we have counts for
16 papers
Approximation and computation of the geodesic Sinkhorn distance
Hugo Lavenant, Jonas Luckhardt, Bernhard Schmitzer
In [H. Lavenant, J. Luckhardt, G. Mordant, B. Schmitzer, L. Tamanini, The Riemannian geometry of Sinkhorn divergences. Ann. Inst. H. Poincaré Anal. Non Linéaire 43 (2026)] we intro…
Semilinear Neumann boundary value problems for measure-valued maps
Aleksei Kroshnin, Hugo Lavenant, Dmitry Vorotnikov
We study the Wasserstein lift of nonlinear Poisson systems with inhomogeneous Neumann boundary conditions. We establish the existence of minimizers using new estimates involving th…
Merging Rate of Opinions via Optimal Transport on Random Measures
Marta Catalano, Hugo Lavenant
Random measures provide flexible parameters for Bayesian nonparametric models. Given two different priors for a random measure, we develop a natural framework to investigate the ra…
Regularized unbalanced optimal transport as entropy minimization with respect to branching Brownian motion
Aymeric Baradat, Hugo Lavenant
We consider the problem of minimizing the entropy of a law with respect to the law of a reference branching Brownian motion under density constraints at an initial and final time.…
A Wasserstein index of dependence for random measures
Marta Catalano, Hugo Lavenant, Antonio Lijoi +1
Optimal transport and Wasserstein distances are flourishing in many scientific fields as a means for comparing and connecting random structures. Here we pioneer the use of an optim…
Convex functions defined on metric spaces are pulled back to subharmonic ones by harmonic maps
Hugo Lavenant, Léonard Monsaingeon, Luca Tamanini +1
If is a harmonic map valued in a metric space and is a convex function, in the sense that it ge…
Towards a mathematical theory of trajectory inference
Hugo Lavenant, Stephen Zhang, Young-Heon Kim +1
We devise a theoretical framework and a numerical method to infer trajectories of a stochastic process from samples of its temporal marginals. This problem arises in the analysis o…
Hidden convexity in a problem of nonlinear elasticity
Nassif Ghoussoub, Young-Heon Kim, Hugo Lavenant +1
We study compressible and incompressible nonlinear elasticity variational problems in a general context. Our main result gives a sufficient condition for an equilibrium to be a glo…
Unconditional convergence for discretizations of dynamical optimal transport
Hugo Lavenant
The dynamical formulation of optimal transport, also known as Benamou-Brenier formulation or Computational Fluid Dynamics formulation, amounts to write the optimal transport proble…
New estimates on the regularity of the pressure in density-constrained Mean Field Games
Hugo Lavenant, Filippo Santambrogio
We consider variational Mean Field Games endowed with a constraint on the maximal density of the distribution of players. Minimizers of the variational formulation are equilibria f…
Dynamical Optimal Transport on Discrete Surfaces
Hugo Lavenant, Sebastian Claici, Edward Chien +1
We propose a technique for interpolating between probability distributions on discrete surfaces, based on the theory of optimal transport. Unlike previous attempts that use linear…
Total Variation Isoperimetric Profiles
Daryl DeFord, Hugo Lavenant, Zachary Schutzman +1
Applications such as political redistricting demand quantitative measures of geometric compactness to distinguish between simple and contorted shapes. While the isoperimetric quoti…
Harmonic mappings valued in the Wasserstein space
Hugo Lavenant
We propose a definition of the Dirichlet energy (which is roughly speaking the integral of the square of the gradient) for mappings mu : Omega -> (P(D), W\_2) defined over a subset…
Optimal density evolution with congestion: L infinity bounds via flow interchange techniques and applications to variational Mean Field Games
Hugo Lavenant, Filippo Santambrogio
We consider minimization problems for curves of measure, with kinetic and potential energy and a congestion penalization, as in the functionals that appear in Mean Field Games with…
Time-convexity of the entropy in the multiphasic formulation of the incompressible euler equation
Hugo Lavenant
We study the multiphasic formulation of the incompressible Euler equation introduced by Brenier: infinitely many phases evolve according to the compressible Euler equation and are…
Mechanical magnetometry of Cobalt nanospheres deposited by focused electron beam at the tip of ultra-soft cantilevers
Hugo Lavenant, Vladimir V. Naletov, Olivier Klein +3
Using focused-electron-beam-induced deposition, Cobalt magnetic nanospheres with diameter ranging between 100 nm and 300 nm are grown at the tip of ultra-soft cantilevers. By monit…