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arXiv · 1807.08838

Fisher Information and Logarithmic Sobolev Inequality for Matrix Valued Functions

Li Gao·Marius Junge·Nicolas LaRacuente
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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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Li Gao, Marius Junge, Nicolas LaRacuente. 2018-07-23. Fisher Information and Logarithmic Sobolev Inequality for Matrix Valued Functions. https://arxiv.org/abs/1807.08838

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