Integer moments of complex Wishart matrices and Hurwitz numbers
| Autor: | Fabio Deelan Cunden, Neil O'Connell, Antoine Dahlqvist |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Wishart distribution Pure mathematics Reflection formula FOS: Physical sciences Combinatorial proof 01 natural sciences Integer QA273 0103 physical sciences FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics 010306 general physics Mathematical Physics Mathematics QA0164 Algebra and Number Theory Probability (math.PR) Inverse-Wishart distribution Zero (complex analysis) Statistical and Nonlinear Physics Mathematical Physics (math-ph) Monotone polygon Combinatorics (math.CO) 010307 mathematical physics Geometry and Topology Random matrix Mathematics - Probability |
| Zdroj: | Annales de l’Institut Henri Poincaré D |
| ISSN: | 2308-5827 |
| DOI: | 10.4171/aihpd/103 |
| Popis: | 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. 19 pages, 1 figure |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|