University of Sussex
Browse
Integrality_Moments.pdf (615.65 kB)

Integer moments of complex Wishart matrices and Hurwitz numbers

Download (615.65 kB)
journal contribution
posted on 2023-06-09, 17:59 authored by Fabio Della Cunden, Antoine DahlqvistAntoine Dahlqvist, Neil O'Connell
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 Hurwitz numbers which count constrained factorisations in the symmetric group. The two expansions can be compared and combined with a duality relation proved in [F. D. Cunden, F. Mezzadri, N. O'Connell and N. J. Simm, arXiv:1805.08760] to obtain: i) a combinatorial proof of the reflection formula between moments of LUE and inverse LUE at genus zero and, ii) a new functional relation between the generating functions of monotone and strictly monotone Hurwitz numbers. The main result resolves the integrality conjecture formulated in [F. D. Cunden, F. Mezzadri, N. J. Simm and P. Vivo, J. Phys. A 49 (2016)] on the time-delay cumulants in quantum chaotic transport. The precise combinatorial description of the cumulants given here may cast new light on the concordance between random matrix and semiclassical theories.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Annales De L'institut Henri Poincaré D

ISSN

2308-5827

Publisher

European Mathematical Society

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Probability and Statistics Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2019-06-06

First Open Access (FOA) Date

2021-03-12

First Compliant Deposit (FCD) Date

2019-06-05

Usage metrics

    University of Sussex (Publications)

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC