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. The argument relies on the uniform smoothness properties of the Schatten trace classes.
© SFoCM 2021. Received 04 April 2020; Revised 04 March 2021; Accepted 17 June 2021; Published 13 August 2021. The authors gratefully acknowledge the funding for this work. DH was supported under NSF Grant DMS-1613861. JNW and RW were supported in part by the Institute for Advanced Study, where some of this research was conducted. JAT was supported under ONR Awards N00014-17-1-2146 and N00014-18-1-2363. RW also received support from AFOSR MURI Award N00014-17-S-F006. Communicated by Alan Edelman.
Submitted - 2003.05437.pdf