TY - JOUR
AB - 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.
AU - GĂ¶tze, Friedrich
AU - Naumov, Alexey
AU - Tikhomirov, Alexander
ID - 2916434
IS - 4B
JF - Bernoulli
KW - central limit theorem
KW - characteristic functions
KW - Fuss-Catalan
KW - distributions
KW - products of random matrices
SN - 1350-7265
TI - Distribution of linear statistics of singular values of the product of random matrices
VL - 23
ER -