44 citations · 145 across the 27 of their papers we have counts for
8 papers · 1 filter
The dynamical Schrödinger problem in abstract metric spaces
Léonard Monsaingeon, Luca Tamanini, Dmitry Vorotnikov
In this paper we introduce the dynamical Schrödinger problem on abstract metric spaces, defined for a wide class of entropy and Fisher information functionals. Under very mild assu…
The Schrödinger problem on the non-commutative Fisher-Rao space
Léonard Monsaingeon, Dmitry Vorotnikov
We present a self-contained and comprehensive study of the Fisher-Rao space of matrix-valued non-commutative probability measures, and of the related Hellinger space. Our non-commu…
Partial differential equations with quadratic nonlinearities viewed as matrix-valued optimal ballistic transport problems
Dmitry Vorotnikov
We study a rather general class of optimal "ballistic" transport problems for matrix-valued measures. These problems naturally arise, in the spirit of \emph{Y. Brenier. Comm. Math.…
Convex Sobolev inequalities related to unbalanced optimal transport
Stanislav Kondratyev, Dmitry Vorotnikov
We study the behaviour of various Lyapunov functionals (relative entropies) along the solutions of a family of nonlinear drift-diffusion-reaction equations coming from statistical…
Spherical Hellinger-Kantorovich gradient flows
Stanislav Kondratyev, Dmitry Vorotnikov
We study nonlinear degenerate parabolic equations of Fokker-Planck type which can be viewed as gradient flows with respect to the recently introduced spherical Hellinger-Kantorovic…
Nonlinear Fokker-Planck equations with reaction as gradient flows of the free energy
Stanislav Kondratyev, Dmitry Vorotnikov
We interpret a class of nonlinear Fokker-Planck equations with reaction as gradient flows over the space of Radon measures equipped with the recently introduced Hellinger-Kantorovi…