# Symmetric function theory and unitary invariant ensembles

@article{Jonnadula2020SymmetricFT, title={Symmetric function theory and unitary invariant ensembles}, author={Bhargavi Jonnadula and Jonathan P. Keating and Francesco Mezzadri}, journal={Journal of Mathematical Physics}, year={2020} }

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…

## 6 Citations

### On the moments of characteristic polynomials

- MathematicsGlasgow 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…

### Laguerre Ensemble: Correlators, Hurwitz Numbers and Hodge Integrals

- MathematicsAnnales 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…

### Maxima of log-correlated fields: some recent developments

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2022

We review recent progress relating to the extreme value statistics of the characteristic polynomials of random matrices associated with the classical compact groups, and of the Riemann zeta-function…

### Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials

- MathematicsLetters 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…

### Quantifying Dip–Ramp–Plateau for the Laguerre Unitary Ensemble Structure Function

- PhysicsCommunications in Mathematical Physics
- 2021

The ensemble average of |∑j=1Neikλj|2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}…

### Exact results and Schur expansions in quiver Chern-Simons-matter theories

- MathematicsJournal of High Energy Physics
- 2020

We study several quiver Chern-Simons-matter theories on the three-sphere, combining the matrix model formulation with a systematic use of Mordell’s integral, computing partition functions and…

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- 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…

### Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials

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- 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…

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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…