Sums of random Hermitian matrices and an inequality by Rudelson
نویسنده
چکیده
i=1 ǫiAi (1) of deterministic Hermitian matrices A1, . . . , An multiplied by random coefficients. Recall that a Rademacher sequence is a sequence {ǫi}i=1 of i.i.d. random variables with ǫ1 uniform over {−1,+1}. A standard Gaussian sequence is a sequence i.i.d. standard Gaussian random variables. Our main goal is to prove the following result. Theorem 1 (proven in Section 3) Given positive integers d, n ∈ N, let A1, . . . , An be deterministic d× d Hermitian matrices and {ǫi}i=1 be either a Rademacher sequence or a standard Gaussian sequence. Define Zn as in (1). Then for all p ∈ [1,+∞),
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