Fisher Information and Logarithmic Sobolev Inequality for Matrix Valued Functions

2018/07/23 by Li Gao, Marius Junge, Gao, Li +3 · 1 citation
Mathematics · #37A35 #46L55 #94A15 #Advanced Mathematical Physics Problems #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Information Theory (cs.IT) #Mathematical Analysis and Transform Methods #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1807.08838

openalex publication_date 2018/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a version of Talagrand's concentration inequality for subordinated sub-Laplacian 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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