Abstract
Abstract
We give a new proof of the equivalence between the dessin partition function and the partition function of the Laguerre unitary ensemble (LUE), originally found by Ambjørn and Chekhov. We also introduce a correction factor for the dessin/LUE partition function, and show that the corrected dessin/LUE partition function is a Dubrovin–Zhang type tau-function of the Toda lattice hierarchy. As an application, we use the approach of Dubrovin and Zhang for the computation of the dessin correlators. In physicists’ terminology, we establish dualities among dessin counting, generalized Penner model, and
P
1
-topological sigma model.
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
Reference109 articles.
1. Matrix integrals, Toda symmetries, Virasoro constraints and orthogonal polynomials;Adler;Duke Math. J.,1995
2. Integrals over classical groups, random permutations, Toda and Toeplitz lattices;Adler;Commun. Pure Appl. Math.,2001
3. Cut-and-join operator representation for Kontsevich–Witten tau-function;Alexandrov;Mod. Phys. Lett. A,2011
4. Weighted Hurwitz numbers and topological recursion;Alexandrov;Commun. Math. Phys.,2020
5. Ramifications of Hurwitz theory, KP integrability and quantum curves;Alexandrov;J. High Energy Phys.,2016
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献