Sampling unitary invariant ensembles
arXiv:1404.0071
Abstract
We develop an algorithm for sampling from the unitary invariant random matrix ensembles. The algorithm is based on the representation of their eigenvalues as a determinantal point process whose kernel is given in terms of orthogonal polynomials. Using this algorithm, statistics beyond those known through analysis are calculable through Monte Carlo simulation. Unexpected phenomena are observed in the simulations.
References in corpus (7)
- Determinantal Processes and Independence
- Random matrices: Universality of local eigenvalue statistics up to the edge
- Universality of a double scaling limit near singular edge points in random matrix models
- Statistical properties of determinantal point processes in high-dimensional Euclidean spaces
- Fast inverse transform sampling in one and two dimensions
- Numerical computation of convolutions in free probability theory
- A Riemann--Hilbert approach to Jacobi operators and Gaussian quadrature