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Laguerre Ensemble: Correlators, Hurwitz Numbers and Hodge Integrals

Gisonni, Massimo
•
Grava, Tamara
•
Ruzza, Giulio
2020
  • journal article

Periodico
ANNALES HENRI POINCARE'
Abstract
We consider the Laguerre partition function, and derive explicit generating func-tions for connected correlators with arbitrary integer powers oftraces in terms of products ofHahn polynomials. It was recently proven in [22] that correlators have a topological expansionin terms of weakly or strictly monotone Hurwitz numbers, that can be explicitly computed fromour formulæ. As a second result we identify the Laguerre partition function with only positivecouplings and a special value of the parameterα=−1/2 with the modified GUE partitionfunction, which has recently been introduced in [28] as a generating function for Hodge inte-grals. This identification provides a direct and new link between monotone Hurwitz numbersand Hodge integrals.
DOI
10.1007/s00023-020-00922-4
WOS
WOS:000542102900001
SCOPUS
2-s2.0-85086698950
Archivio
http://hdl.handle.net/20.500.11767/112949
Diritti
open access
Soggetti
  • Laguerre unitary ense...

  • Hurwitz numbers and H...

  • orthogonal polynomial...

Web of Science© citazioni
7
Data di acquisizione
Jun 6, 2022
Visualizzazioni
2
Data di acquisizione
Jun 8, 2022
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