• Corpus ID: 51767183

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}
}
• Published 1 April 2014
• Mathematics
• arXiv: Mathematical Physics
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.

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References

SHOWING 1-10 OF 35 REFERENCES

• Mathematics
• 2009
In this paper, we consider the universality of the local eigenvalue statistics of random matrices. Our main result shows that these statistics are determined by the first four moments of the
The technique is used in an empirical study of two methods for estimating the condition number of a matrix in the group of orthogonal matrices.
• Computer Science
• 2013
We develop a computationally efficient and robust algorithm for generating pseudo-random samples from a broad class of smooth probability distributions in one and two dimensions. The algorithm is
• Mathematics
• 2009
This book features a unified derivation of the mathematical theory of the three classical types of invariant random matrix ensembles - orthogonal, unitary, and symplectic. The authors follow the
• Mathematics
• 2012
Recently, a general approach to solving Riemann–Hilbert problems numerically has been developed. We review this numerical framework and apply it to the calculation of orthogonal polynomials on the
• Computer Science
• 2002
This paper constructs tridiagonal random matrix models for general (β>0) β-Hermite (Gaussian) and β-Laguerre (Wishart) ensembles. These generalize the well-known Gaussian and Wishart models for
• Mathematics
• 2011
We study a family of distributions that arise in critical unitary random matrix ensembles. They are expressed as Fredholm determinants and describe the limiting distribution of the largest eigenvalue
• Mathematics, Computer Science
Found. Comput. Math.
• 2008
The mathematics of the polynomial method is developed which allows us to describe the class of algebraic matrices by its generators and map the constructive approach when proving algebraicity into a software implementation that is available for download in the form of the RMTool random matrix “calculator” package.
• Mathematics
• 2006
We give a probabilistic introduction to determinantal and per- manental point processes. Determinantal processes arise in physics (fermions, eigenvalues of random matrices) and in combinatorics