The dynamical Schrödinger problem in abstract metric spaces

Léonard Monsaingeon; Luca Tamanini; Dmitry Vorotnikov

doi:10.1016/j.aim.2023.109100

The dynamical Schrödinger problem in abstract metric spaces

Léonard Monsaingeon
, Luca Tamanini
, Dmitry Vorotnikov

University of Lisbon
University of Coimbra

Research output: Contribution to journal › Article

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.

Original language	English
Pages (from-to)	N/A-N/A
Journal	Advances in Mathematics
DOIs	https://doi.org/10.1016/j.aim.2023.109100
Publication status	Published - 2023

Keywords

Fisher information
Gamma-convergence
Gradient flows
Metric geometry
Optimal transport

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10.1016/j.aim.2023.109100

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title = "The dynamical Schr{\"o}dinger problem in abstract metric spaces",

abstract = "In this paper we introduce the dynamical Schr{\"o}dinger 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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year = "2023",

doi = "10.1016/j.aim.2023.109100",

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T1 - The dynamical Schrödinger problem in abstract metric spaces

AU - Monsaingeon, Léonard

AU - Tamanini, Luca

AU - Vorotnikov, Dmitry

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - Fisher information

KW - Gamma-convergence

KW - Gradient flows

KW - Metric geometry

KW - Optimal transport

KW - Fisher information

KW - Gamma-convergence

KW - Gradient flows

KW - Metric geometry

KW - Optimal transport

UR - http://hdl.handle.net/10807/236918

U2 - 10.1016/j.aim.2023.109100

DO - 10.1016/j.aim.2023.109100

M3 - Article

SN - 0001-8708

SP - N/A-N/A

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

The dynamical Schrödinger problem in abstract metric spaces

Abstract

Keywords

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