Moments of the eigenvalue densities and of the secular coefficients of β-ensembles
journal contributionposted on 23.07.2018, 10:11 by Francesco Mezzadri, Alexi K. Reynolds, Brian WinnBrian Winn
© 2017 IOP Publishing Ltd & London Mathematical Society.We compute explicit formulae for the moments of the densities of the eigenvalues of the classical β-ensembles for finite matrix dimension as well as the expectation values of the coefficients of the characteristic polynomials. In particular, the moments are linear combinations of averages of Jack polynomials, whose coefficients are related to specific examples of Jack characters.
FM was partially supported by EPSRC research grant EP/L010305/1.
- Mathematical Sciences