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Seminar: Brendan Farrell

Department of Statistics Seminar Series
January 9, 2013
All Day
Cockins Hall (CH), Room 240

Title

Local Eigenvalue Density for General MANOVA Matrices

Speaker

Brendan Farrell, CalTech

Abstract

Note: This seminar is primarily hosted by the Mathematics Department.

MANOVA matrices are a fundamental matrix form in statistics. When the matrix entries are Gaussian, the joint eigenvalue density for this form is known in classical random matrix theory as the Jacobi ensemble. Previous results for these matrices have only addressed the case when the matrix entries are Gaussian. We present the first universality result for this matrix form: for entries satisfying general conditions, we show that the eigenvalue density of a general MANOVA matrix converges at the smallest possible scale to the limiting density of the Jacobi ensemble. This result is the analogue to the Wigner semicircle law or the Marchenko-Pastur law. We briefly discuss the relationship to the geometry of random subspaces and discrete harmonic analysis.