TY - JOUR
T1 - Fisher Information and Logarithmic Sobolev Inequality for Matrix-Valued Functions
AU - Gao, Li
AU - Junge, Marius
AU - LaRacuente, Nicholas
N1 - Funding Information:
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.
Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
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.
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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 -