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.

Laguerre Ensemble: Correlators, Hurwitz Numbers and Hodge Integrals / Gisonni, Massimo; Grava, Tamara; Ruzza, Giulio. - In: ANNALES HENRI POINCARE'. - ISSN 1424-0637. - 21(2020), pp. 3285-3339. [10.1007/s00023-020-00922-4]

Laguerre Ensemble: Correlators, Hurwitz Numbers and Hodge Integrals

Gisonni, Massimo;Grava, Tamara;Ruzza, Giulio
2020

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.
ANNALES HENRI POINCARE'
21
3285
3339
https://link.springer.com/article/10.1007/s00023-020-00922-4
Gisonni, Massimo; Grava, Tamara; Ruzza, Giulio
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/112949
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