The Expected Norm of a Sum of Independent Random Matrices: An Elementary Approach

By Joel A. Tropp. 2015

69 citations recorded by the source corpus.

In contemporary applied and computational mathematics, a frequent challenge is to bound the expectation of the spectral norm of a sum of independent random matrices. This quantity is controlled by the norm of the expected square of the random matrix and the expectation of the maximum squared norm achieved by one of the summands; there is also a weak dependence on the dimension of the random matrix. The purpose of this paper is to give a complete, elementary proof of this important inequality.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Statistics and Probability

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Citations in the corpus

Matrix concentration inequalities and free probability (2021, background): “This idea arises clearly in proofs of these inequalities [39, 40, 43]: the key step is application of trace inequalities that permute the order of the matrices Ai, which become equalities when all Ai commute.”
One-Shot Federated Learning: Theoretical Limits and Algorithms to Achieve Them (2019, background): “It follows that Lemma 22 is an immediate Corollary of Theorem 1 in (Tropp, 2016) by letting v ( · ) = n , L = 1 , and C ( d ) ≤ 12 log( d + 1) .”
Randomized numerical linear algebra: Foundations and algorithms (2020, methodology): “J. A. Tropp (2016), The expected norm of a sum of independent random matrices: an elementary approach, in High dimensional probability VII, Vol. 71 of Progr.”