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
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References
SHOWING 1-10 OF 68 REFERENCES
On the Averages of Characteristic Polynomials From Classical Groups
- Mathematics
- 2005
We provide an elementary and self-contained derivation of formulae for averages of products and ratios of characteristic polynomials of random matrices from classical groups using classical results…
Integer moments of complex Wishart matrices and Hurwitz numbers
- MathematicsAnnales de l’Institut Henri Poincaré D
- 2018
We give formulae for the cumulants of complex Wishart (LUE) and inverse Wishart matrices (inverse LUE). Their large-N expansions are generating functions of double (strictly and weakly) monotone…
On the eigenvalues of random matrices
- MathematicsJournal of Applied Probability
- 1994
Let M be a random matrix chosen from Haar measure on the unitary group Un. Let Z = X + iY be a standard complex normal random variable with X and Y independent, mean 0 and variance ½ normal…
Jacobi-Trudy formula for generalised Schur polynomials
- Mathematics
- 2009
Jacobi-Trudy formula for a generalisation of Schur polynomials related to any sequence of orthogonal polynomials in one variable is given. As a corollary we have Giambelli formula for generalised…
ON RANDOM MATRICES FROM THE COMPACT CLASSICAL GROUPS
- Mathematics
- 1997
If M is a matrix taken randomly with respect to normalized Haar measure on U(n), O(n) or Sp(n), then the real and imaginary parts of the random variables Tr(Mk), k > 1, converge to independent normal…
Symmetric functions and Hall polynomials
- Mathematics
- 1979
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…
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…
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…
Auto-correlation functions of Sato–Tate distributions and identities of symplectic characters
- MathematicsAdvances in Mathematics
- 2022
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…