Event Type:

Probability Seminar

Date/Time:

Thursday, April 26, 2007 - 07:00

Location:

Kidder 364

Guest Speaker:

Institution:

University of Washington

Abstract:

β-Hermite, -Laguerre, and -Jacobi ensembles are generalizations of the Gaussian, central Wishart, and MANOVA matrices, with applicability in fields like statistical mechanics and traffic pattern analysis. Matrix models for these β-ensembles have been discovered relatively recently, and the implications of this discovery for the study of the β-ensemble eigenstatistics cannot be understated. In this talk, we will show how these matrix models were discovered, and sketch the proof that the eigenvalues of the β-Hermite matrix have joint eigenvalue distribution given by the β-Hermite ensemble (which, for β=1,2, respectively 4, are the same as the eigenvalue distributions of the Gaussian Orthogonal, Unitary, respectively Symplectic ensembles).