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

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10.1007/s00023-020-00947-9

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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 = "LG and NL acknowledge support from NSF Grant DMS-1700168. NL is supported by NSF Graduate Research Fellowship Program DMS-1144245. MJ is partially supported by NSF Grant DMS 1800872.",

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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.

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Fisher Information and Logarithmic Sobolev Inequality for Matrix-Valued Functions

Abstract

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