In this paper we introduce the dynamical Schrödinger prob-lem, defined for a wide class of entropy and Fisher information functionals, as a geometric problem on abstract metric spaces. Under very mild assumptions we prove a generic Γ-convergence result towards the geodesic problem as the noise parameter ε↓0. We also study the dependence of the entropic cost on the parameter ε. Some examples and applications are discussed.
Monsaingeon, L., Tamanini, L., Vorotnikov, D., The dynamical Schrödinger problem in abstract metric spaces, <<ADVANCES IN MATHEMATICS>>, 2023; (426): N/A-N/A. [doi:10.1016/j.aim.2023.109100] [https://hdl.handle.net/10807/236918]
The dynamical Schrödinger problem in abstract metric spaces
Tamanini, Luca;
2023
Abstract
In this paper we introduce the dynamical Schrödinger prob-lem, defined for a wide class of entropy and Fisher information functionals, as a geometric problem on abstract metric spaces. Under very mild assumptions we prove a generic Γ-convergence result towards the geodesic problem as the noise parameter ε↓0. We also study the dependence of the entropic cost on the parameter ε. Some examples and applications are discussed.
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