Distribution of linear statistics of singular values of the product of random matrices

Götze F, Naumov A, Tikhomirov A (2017)
Bernoulli 23(4B): 3067-3113.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
In this paper we consider the product of two independent random matrices X-(1) and X-(2). Assume that X-jk((q)), 1 <= j,k <= n, q = 1, 2, are i.i.d. random variables with EXjk(q)) = 0, Var X-jk((q)) = 1. Denote b s(1)(W), ..., s(n)(W) the singular values of W := 1/nX((1))X((2)). We prove the central limit theorem for linear statistics of the squared singular values s(1)(2)(W), ..., s(n)(2) (W) showing that the limiting variance depends on kappa(4) := E(X-11((1)))(4) - 3.
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Zeitschriftentitel
Bernoulli
Band
23
Ausgabe
4B
Seite(n)
3067-3113
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Götze F, Naumov A, Tikhomirov A. Distribution of linear statistics of singular values of the product of random matrices. Bernoulli. 2017;23(4B):3067-3113.
Götze, F., Naumov, A., & Tikhomirov, A. (2017). Distribution of linear statistics of singular values of the product of random matrices. Bernoulli, 23(4B), 3067-3113. doi:10.3150/16-BEJ837
Götze, F., Naumov, A., and Tikhomirov, A. (2017). Distribution of linear statistics of singular values of the product of random matrices. Bernoulli 23, 3067-3113.
Götze, F., Naumov, A., & Tikhomirov, A., 2017. Distribution of linear statistics of singular values of the product of random matrices. Bernoulli, 23(4B), p 3067-3113.
F. Götze, A. Naumov, and A. Tikhomirov, “Distribution of linear statistics of singular values of the product of random matrices”, Bernoulli, vol. 23, 2017, pp. 3067-3113.
Götze, F., Naumov, A., Tikhomirov, A.: Distribution of linear statistics of singular values of the product of random matrices. Bernoulli. 23, 3067-3113 (2017).
Götze, Friedrich, Naumov, Alexey, and Tikhomirov, Alexander. “Distribution of linear statistics of singular values of the product of random matrices”. Bernoulli 23.4B (2017): 3067-3113.