Antti Knowles (ETHZ): Random matrices and multivariate statistics

Academic or specialist Colloquium / Congress / Forum

I review some applications of random matrix theory to multivariate statistics. Suppose one is interested in the covariance matrix of a random vector whose distribution is unknown. In order to determine the covariances from empirical observations, one approximates them using empirical averages obtained from a series of measurements. The resulting sample covariance matrix is random, and its relationship with the true covariance matrix rather intricate. I outline some recent progress in understanding the behaviour of sample covariance matrices. The cornerstone of the proofs is an anisotropic local law for the resolvent. Applications include the Tracy-Widom distribution of eigenvalues near the spectral edges.

When? 07.10.2014 17:15
Where? PER 08 Phys 2.52
Chemin du Musée 3
1700 Fribourg
Contact Department of Mathematics