# Sampling unitary invariant ensembles

@article{Olver2014SamplingUI, title={Sampling unitary invariant ensembles}, author={Sheehan Olver and Raj Rao Nadakuditi and Thomas Trogdon}, journal={arXiv: Mathematical Physics}, year={2014} }

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.

## 5 Citations

### Fast sampling from ˇ -ensembles

- Computer Science
- 2020

The experimental results support a conjecture by Krishnapur et al. (Commun Pure Appl Math 69(1): 145–199, 2016), that the Gibbs chain on Jacobi matrices of size N mixes in O ( log N ) .

### Some Open Problems in Random Matrix Theory and the Theory of Integrable Systems. II

- Mathematics
- 2017

We describe a list of open problems in random matrix theory and integrable systems which was presented at the conference ``Integrable Systems, Random Matrices, and Applications'' at the Courant…

### Fast sampling from $$\beta $$ β -ensembles

- Computer ScienceStat. Comput.
- 2021

The experimental results support a conjecture by Krishnapur et al. (Commun Pure Appl Math 69(1): 145–199, 2016), that the Gibbs chain on Jacobi matrices of size N mixes in $\mathcal {O}(\log N)$$ O ( log N ) .

### Universality in numerical computations with random data

- Computer ScienceProceedings of the National Academy of Sciences
- 2014

Evidence for universality in numerical computations with random data, which includes six standard numerical algorithms as well as a model of neural computation and decision-making, is presented.

### N A ] 1 6 Ju l 2 01 4 Universality in Numerical Computations with Random Data . Case Studies

- Mathematics
- 2014

The authors present evidence for universality in numerical computations with random data. Given a (possibly stochastic) numerical algorithm with random input data, the time (or number of iterations)…

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