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

作者：Goetze Friedrich; Naumov Alexey; Tikhomirov Alexander

来源：Bernoulli, 2017, 23(4B): 3067-3113.

DOI：10.3150/16-BEJ837

• central limit theorem
• characteristic functions
• Fuss-Catalan distributions
• products of random matrices

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.

• 出版日期2017-11