Matrix Concentration for Products

This paper develops nonasymptotic growth and concentration bounds for a product of independent random matrices. These results sharpen and generalize recent work of Henriksen–Ward, and they are similar in spirit to the results of Ahlswede–Winter and of Tropp for a sum of independent random matrices....

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Veröffentlicht in:	Foundations of computational mathematics 2022-12, Vol.22 (6), p.1767-1799
Hauptverfasser:	Huang, De, Niles-Weed, Jonathan, Tropp, Joel A., Ward, Rachel
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics Computer Science Economics Linear and Multilinear Algebras Math Applications in Computer Science Mathematical research Mathematics Mathematics and Statistics Matrices Matrix Theory Numerical Analysis Smoothness
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Beschreibung
Zusammenfassung:	This paper develops nonasymptotic growth and concentration bounds for a product of independent random matrices. These results sharpen and generalize recent work of Henriksen–Ward, and they are similar in spirit to the results of Ahlswede–Winter and of Tropp for a sum of independent random matrices. The argument relies on the uniform smoothness properties of the Schatten trace classes.
ISSN:	1615-3375 1615-3383
DOI:	10.1007/s10208-021-09533-9