Fisher Information and Logarithmic Sobolev Inequality for Matrix-Valued Functions

Li Gao; Marius Junge; Nicholas LaRacuente

doi:10.1007/s00023-020-00947-9

Fisher Information and Logarithmic Sobolev Inequality for Matrix-Valued Functions

Li Gao, Marius Junge, Nicholas LaRacuente

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove a version of Talagrand’s concentration inequality for subordinated sub-Laplacians on a compact Riemannian manifold using tools from noncommutative geometry. As an application, motivated by quantum information theory, we show that on a finite-dimensional matrix algebra the set of self-adjoint generators satisfying a tensor stable modified logarithmic Sobolev inequality is dense.

Original language	English (US)
Pages (from-to)	3409-3478
Number of pages	70
Journal	Annales Henri Poincare
Volume	21
Issue number	11
Early online date	Sep 25 2020
DOIs	https://doi.org/10.1007/s00023-020-00947-9
State	Published - Nov 1 2020

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Nuclear and High Energy Physics
Mathematical Physics

Online availability

10.1007/s00023-020-00947-9

Library availability

Discover UIUC Full Text

Cite this

@article{c6120ea0b0fd46ceabac13509ef32ad6,

title = "Fisher Information and Logarithmic Sobolev Inequality for Matrix-Valued Functions",

abstract = "We prove a version of Talagrand{\textquoteright}s concentration inequality for subordinated sub-Laplacians on a compact Riemannian manifold using tools from noncommutative geometry. As an application, motivated by quantum information theory, we show that on a finite-dimensional matrix algebra the set of self-adjoint generators satisfying a tensor stable modified logarithmic Sobolev inequality is dense.",

author = "Li Gao and Marius Junge and Nicholas LaRacuente",

note = "Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.",

year = "2020",

month = nov,

day = "1",

doi = "10.1007/s00023-020-00947-9",

language = "English (US)",

volume = "21",

pages = "3409--3478",

journal = "Annales Henri Poincare",

issn = "1424-0637",

publisher = "Birkhauser Verlag Basel",

number = "11",

}

TY - JOUR

T1 - Fisher Information and Logarithmic Sobolev Inequality for Matrix-Valued Functions

AU - Gao, Li

AU - Junge, Marius

AU - LaRacuente, Nicholas

PY - 2020/11/1

Y1 - 2020/11/1

N2 - We prove a version of Talagrand’s concentration inequality for subordinated sub-Laplacians on a compact Riemannian manifold using tools from noncommutative geometry. As an application, motivated by quantum information theory, we show that on a finite-dimensional matrix algebra the set of self-adjoint generators satisfying a tensor stable modified logarithmic Sobolev inequality is dense.

AB - We prove a version of Talagrand’s concentration inequality for subordinated sub-Laplacians on a compact Riemannian manifold using tools from noncommutative geometry. As an application, motivated by quantum information theory, we show that on a finite-dimensional matrix algebra the set of self-adjoint generators satisfying a tensor stable modified logarithmic Sobolev inequality is dense.

UR - http://www.scopus.com/inward/record.url?scp=85091534413&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85091534413&partnerID=8YFLogxK

U2 - 10.1007/s00023-020-00947-9

DO - 10.1007/s00023-020-00947-9

M3 - Article

AN - SCOPUS:85091534413

SN - 1424-0637

VL - 21

SP - 3409

EP - 3478

JO - Annales Henri Poincare

JF - Annales Henri Poincare

IS - 11

ER -

Fisher Information and Logarithmic Sobolev Inequality for Matrix-Valued Functions

Abstract

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Cite this