# Of Pfaffians, correlation functions and a geometrical triumvirate of real random matrices

*by Anthony Mays*

*Institution:*University of Melbourne

*Date: Tue 30th August 2011*

*Time: 12:00 PM*

*Location: Richard Berry Building - Russel Love Theatre*

*Abstract*: A random matrix is, broadly speaking, a matrix with entries randomly

chosen from some distribution. In the non-random case eigenvalues can

occur anywhere in the complex plane, but, remarkably, random elements

imply predictable behaviour, albeit in a probabilistic sense.

Correlation functions are one measure of a probabilistic

characterisation and we discuss a 5-part scheme, based upon orthogonal

polynomials, to calculate the eigenvalue correlation functions. We apply

this scheme to three ensembles of random matrices, each of which can be

identified with one of the surfaces of constant Gaussian curvature: the

plane, the sphere and the anti- or pseudo-sphere. We will be using real

random matrices, which possess the added complication of having a finite

probability of real eigenvalues.

This talk aims to be accessible, and to that end we will start with a

general overview of random matrices and then discuss the 5-step method,

hopefully keeping technicalities to a minimum, and with plenty of pictures.

*For More Information:* contact Guoqi Qian, email: g.qian@ms.unimelb.edu.au