Engineering

Pure mathematics

Materials science

Riemannian manifold

Mechanical engineering

Matrix (chemical analysis)

Tensor (intrinsic definition)

Mathematics

Noncommutative geometry

Mathematical analysis

Composite material

Logarithm

Manifold (fluid mechanics)

Algebra over a field

Annales Henri Poincaré

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.

Fisher Information and Logarithmic Sobolev Inequality for Matrix-Valued Functions