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Full title: On the fluctuations of the linear eigenvalue statistics of the sample covariance matrices corresponding to data with a tensor product structure
Abstract: Consider a vector that is a tensor product of two n-dimensional copies of a random vector Y, and the corresponding sample covariance matrix with the number of data points proportional to n. Under some additional moment conditions, we study the fluctuations of the linear eigenvalue statistics of such matrices as n goes to infinity. In particular, we show that taking Y from the normal distribution or from the uniform distribution on the unit sphere results in different orders of fluctuations of the resolvent traces. We use this result to prove the CLT for the corresponding, properly normalized and centralized, linear eigenvalue statistics. The talk is based on the joint work with Alicja Dembczak-Kolodziejczyk.