# Moments of Random Matrices and Hypergeometric Orthogonal Polynomials

@article{Cunden2018MomentsOR, title={Moments of Random Matrices and Hypergeometric Orthogonal Polynomials}, author={Fabio Deelan Cunden and Francesco Mezzadri and Neil O'Connell and N. J. Simm}, journal={Communications in Mathematical Physics}, year={2018}, pages={1-55} }

We establish a new connection between moments of $${n \times n}$$n×n random matrices Xn and hypergeometric orthogonal polynomials. Specifically, we consider moments $${\mathbb{E}{\rm Tr} X_n^{-s}}$$ETrXn-s as a function of the complex variable $${s \in \mathbb{C}}$$s∈C , whose analytic structure we describe completely. We discover several remarkable features, including a reflection symmetry (or functional equation), zeros on a critical line in the complex plane, and orthogonality relations. An… CONTINUE READING

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