|Date: Wednesday, November 02, 2011
Location: 3866 East Hall (3:40 PM to 5:00 PM)
Title: Middle eigenvalues and eigenvectors in spiked random matrix models
Abstract: We consider low-rank perturbations of symmetric random matrices and examine how the eigenvalues and eigenvectors of the perturbed matrix are related to the eigenvalues and eigenvectors of the low-rank portion. What emerges from the analysis is the relevance of the level sets of the Cauchy transform of the spectral measure of the eigenvalues of random matrix and its role in quantifying the bias and phase transitions in the leading eigenvectors and the eigenvalues. Modifying the spectral measure ever so slightly brings into focus the surprising (and perhaps unanticipated in applications) importance of the middle eigenvalues and eigenvectors of such matrices.
Speaker: Raj Rao
Institution: UM, EECS