Student Probability Seminar

Eigenvalue Statistics of Wigner Ensembles and Unitary Ensembles

Speaker: Oliver Conway

Location: Warren Weaver Hall 1314

Date: Thursday, April 25, 2013, 3:30 p.m.

Synopsis:

An ensemble of Hermitian matrices is a sequence of independent random variables $${X_N}_{N=1}^\infty$$ that each take values in the $$N \times N$$ Hermitian matrices. There are two types of ensembles that are of particular interest: Wigner ensembles, whose entries are independent random variables, and unitary ensembles, which are invariant under conjugation by unitary matrices (changes of basis). The most commonly considered ensemble, the Gaussian Unitary Ensemble (GUE), is the only ensemble that belongs to both categories. In this talk, we will consider the large $$N$$ behavior of the eigenvalues of the matrices in these two types of ensembles.