Laguerre Ensemble: Correlators, Hurwitz Numbers and Hodge Integrals

Massimo Gisonni, Tamara Grava, Giulio Ruzza

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Abstract

We consider the Laguerre partition function, and derive explicit generating functions for connected correlators with arbitrary integer powers of traces in terms of products of Hahn polynomials. It was recently proven that correlators have a topological expansion in terms of weakly or strictly monotone Hurwitz numbers, that can be explicitly computed from our formulae. As a second result we identify the Laguerre partition function with only positive couplings and a special value of the parameter α=−1/2 with the modified GUE partition function, which has recently been introduced as a generating function of Hodge integrals. This identification provides a direct and new link between monotone Hurwitz numbers and Hodge integrals.
Original languageEnglish
Pages (from-to)3285 - 3339
Number of pages55
JournalAnnales Henri Poincaré
Volume2020
Issue number21
DOIs
Publication statusPublished - 22 Jun 2020

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