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Published April 22, 2015 | Submitted
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Second-Order Matrix Concentration Inequalities

Tropp, Joel A.


Matrix concentration inequalities give bounds for the spectral-norm deviation of a random matrix from its expected value. These results have a weak dimensional dependence that is sometimes, but not always, necessary. This paper identifies one of the sources of the dimensional term and exploits this insight to develop sharper matrix concentration inequalities. In particular, this analysis delivers two refinements of the matrix Khintchine inequality that use information beyond the matrix variance to reduce or eliminate the dimensional dependence.

Additional Information

Date: 13 March 2015. Revised 21 April 2015 and 3 August 2016. Afonso Bandeira is responsible for the argument in Section 4.3, and Ramon van Handel has offered critical comments. Parts of this research were completed at Mathematisches Forschungsinstitut Oberwolfach (MFO) and at Instituto Nacional de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro. The author gratefully acknowledges support from ONR award N00014-11-1002, a Sloan Research Fellowship, and the Gordon & Betty Moore Foundation.

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August 20, 2023
August 20, 2023