Fluctuations of Linear Eigenvalue Statistics in Sample Covariance Matrices - Tensor Product Data

Explore the fluctuations of linear eigenvalue statistics in sample covariance matrices with tensor product structure data. Delve into a 56-minute lecture that examines a vector formed by the tensor product of two n-dimensional copies of a random vector Y and its corresponding sample covariance matrix. Discover how the number of data points proportional to n affects the fluctuations as n approaches infinity. Learn about the different orders of fluctuations in resolvent traces when Y is taken from normal distribution versus uniform distribution on the unit sphere. Gain insights into the Central Limit Theorem (CLT) for properly normalized and centralized linear eigenvalue statistics. Understand the implications of this research, based on joint work with Alicja Dembczak-Kolodziejczyk, presented by Anna Lytova at the Hausdorff Center for Mathematics.