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

Risultato della ricerca: Contributo in rivista › Articolo

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.

Lingua originale	Inglese
pagine (da-a)	N/A-N/A
Rivista	Advances in Mathematics
DOI	https://doi.org/10.1016/j.aim.2023.109100
Stato di pubblicazione	Pubblicato - 2023

Keywords

Fisher information
Gamma-convergence
Gradient flows
Metric geometry
Optimal transport

Accesso al documento

10.1016/j.aim.2023.109100

Altri file e collegamenti

Open Access link a IRIS PubliCatt

Cita questo

@article{f7f0f2d6dafc47b2b2bf1313f4f1847b,

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.",

keywords = "Fisher information, Gamma-convergence, Gradient flows, Metric geometry, Optimal transport, Fisher information, Gamma-convergence, Gradient flows, Metric geometry, Optimal transport",

author = "L{\'e}onard Monsaingeon and Luca Tamanini and Dmitry Vorotnikov",

year = "2023",

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

language = "English",

pages = "N/A--N/A",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

}

TY - JOUR

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

Accesso al documento

Altri file e collegamenti

Fingerprint

Cita questo