# Symmetric function theory and unitary invariant ensembles

@article{Jonnadula2020SymmetricFT,
title={Symmetric function theory and unitary invariant ensembles},
journal={Journal of Mathematical Physics},
year={2020}
}
• Published 5 March 2020
• Mathematics
• Journal of Mathematical Physics
Representation theory and the theory of symmetric functions have played a central role in Random Matrix Theory in the computation of quantities such as joint moments of traces and joint moments of characteristic polynomials of matrices drawn from the Circular Unitary Ensemble and other Circular Ensembles related to the classical compact groups. The reason is that they enable the derivation of exact formulae, which then provide a route to calculating the large-matrix asymptotics of these…
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The ensemble average of |∑j=1Neikλj|2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}
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I. Symmetric functions II. Hall polynomials III. HallLittlewood symmetric functions IV. The characters of GLn over a finite field V. The Hecke ring of GLn over a finite field VI. Symmetric functions
• Mathematics
Glasgow Mathematical Journal
• 2022
We calculate the moments of the characteristic polynomials of $N\times N$ matrices drawn from the Hermitian ensembles of Random Matrix Theory, at a position t in the bulk of the
• Mathematics
Letters in Mathematical Physics
• 2021
We express the topological expansion of the Jacobi Unitary Ensemble in terms of triple monotone Hurwitz numbers. This completes the combinatorial interpretation of the topological expansion of the
• Mathematics
Annales Henri Poincaré
• 2020
We consider the Laguerre partition function and derive explicit generating functions for connected correlators with arbitrary integer powers of traces in terms of products of Hahn polynomials. It was