This article is cited in 2 papers

Integrals of tau functions: A round dance tau function and multimatrix integrals

A. Yu. Orlov<sup>ab

a</sup> Shirshov Institute of Oceanology, Russian Academy of Sciences, Moscow, Russia
^b Alikhanov Institute for Theoretical and Experimental Physics, National Research Center "Kurchatov Institute," Moscow, Russia

Abstract: A multimatrix model can be built on two ingredients: the choice of an embedded graph and the choice of the integrand, that is, a tau function. We compare the simplest nontrivial tau function of the Toda lattice and the simplest nontrivial tau function of the $\mathcal N$-component Toda lattice in the context of their application to multimatrix integrals.

Keywords: tau function, special solution of the multicomponent KP hierarchy, embedded graph, Hurwitz number.

Received: 20.11.2022
Revised: 15.02.2023

DOI: 10.4213/tmf10406

 English version: Theoretical and Mathematical Physics, 2023, 215:3, 784–792

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