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.File | Dimensione | Formato | |
---|---|---|---|
LUE_arxiv.pdf
accesso aperto
Descrizione: Artiolo principale
Licenza:
Non specificato
|
696.05 kB | Adobe PDF | Visualizza/Apri |
Gisonni2020_Article_LaguerreEnsembleCorrelatorsHur.pdf
accesso aperto
Descrizione: articolo principale vesione editoriale
Licenza:
Creative commons
|
833.54 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.