FoCM 2014 conference

Workshop B6 - Random Matrices

December 17, 14:30 ~ 14:55 - Room B12

## Sampling unitary ensembles

### Sheehan Olver

### The University of Sydney, Australia - Sheehan.Olver@sydney.edu.au

We develop a computationally efficient algorithm for sampling from a broad class of unitary random matrix ensembles that includes but goes well beyond the straightforward to sample Gaussian Unitary Ensemble (GUE). The algorithm exploits the fact that the eigenvalues of unitary ensembles (UEs) can be represented as a determinantal point process whose kernel is given in terms of orthogonal polynomials. Consequently, our algorithm can be used to sample from UEs for which the associated orthogonal polynomials can be numerically computed efficiently. By facilitating high accuracy sampling of non-classical UEs, the algorithm can aid in the experimentation-based formulation (or refutation) of universality conjectures involving eigenvalue statistics that might presently be unamenable to analysis. Examples of such experiments are included.

Joint work with Raj Rao (University of Michigan) and Thomas Trogdon (New York University).