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Web page of Aymeric Baradat

Research

Publications

  1. Convergence of the Sinkhorn algorithm when the Schrödinger problem has no solution (2023).
    arXiv.
    With Elias Ventre, accepted in Annales de la Faculté des Sciences de Toulouse.
  2. Monge-Ampère gravitation as a Γ-limit of good rate functions (2020).
    arXiv, journal.
    With Yann Brenier and Luigi Ambrosio, Analysis & PDEs.
  3. Regularized unbalanced optimal transport as entropy minimization with respect to branching Brownian motion (2021).
    arXiv.
    With Hugo Lavenant, accepted in Astérique.
  4. Γ-convergence for a class of action functionals induced by gradients of convex functions (2021).
    arXiv, journal.
    With Yann Brenier and Luigi Ambrosio, Rendiconti Lincei - Matematica e Applicazioni.
  5. Nonlinear instability in Vlasov type equations around rough velocity profiles (2020).
    arXiv, journal.
    Annales de l'Institut Henri Poincaré C Analyse non-linéaire.
  6. On the existence of a scalar pressure field in the Bredinger problem (2020).
    arXiv, journal.
    SIAM Journal on Mathematical Analysis.
  7. Small noise limit and convexity for generalized incompressible flows, Schrödinger problems, and optimal transport (2019).
    arXiv, journal.
    With Léonard Monsaingeon, Archive of Rational Mechanics and Analysis.
  8. Continuous dependence of the pressure field with respect to endpoints for ideal incompressible fluids (2019).
    arXiv, journal.
    Calculus of Variations and Partial Differential Equations.

Preprints

PhD

I defended my PhD, entitled Incompressible optimal transport: dependence to the data and entropic regularization and made under the supervision of Yann Brenier and Daniel Han-Kwan in June 2019. Here is the definitive version of the text, and here you can find the slides of the defense (in french).

Other productions (in french)

  • Problèmes de minimisation d'entropie avec contraintes.
    (My second master thesis, in probability.) pdf, Slides of the defense.
  • Équation d’Euler et principe de moindre action.
    (An introdution to my field of research.) pdf.
  • Méthodes variationnelles appliquées à la résolution et à l’étude des solutions d’équations de la mécanique des fluides.
    (My first master thesis, in analysis.) pdf.