# Generating series for GUE correlators

@article{Dubrovin2016GeneratingSF, title={Generating series for GUE correlators}, author={Boris Dubrovin and Di Yang}, journal={Letters in Mathematical Physics}, year={2016}, volume={107}, pages={1971-2012} }

We extend to the Toda lattice hierarchy the approach of Bertola et al. (Phys D Nonlinear Phenom 327:30–57, 2016; IMRN, 2016) to computation of logarithmic derivatives of tau-functions in terms of the so-called matrix resolvents of the corresponding difference Lax operator. As a particular application we obtain explicit generating series for connected GUE correlators. On this basis an efficient recursive procedure for computing the correlators in full genera is developed.

#### 22 Citations

On tau-functions for the Toda lattice hierarchy

- Physics, Mathematics
- Letters in Mathematical Physics
- 2019

We extend a recent result of Dubrovin et al. in On tau-functions for the KdV hierarchy, arXiv:1812.08488 to the Toda lattice hierarchy. Namely, for an arbitrary solution to the Toda lattice… Expand

On tau-functions for the KdV hierarchy

- Physics, Mathematics
- 2018

For an arbitrary solution to the KdV hierarchy, the generating series of logarithmic derivatives of the tau-function of the solution can be expressed by the basic matrix resolvent via algebraic… Expand

Hodge–GUE Correspondence and the Discrete KdV Equation

- Physics, Mathematics
- 2016

We prove the conjectural relationship recently proposed in [9] between certain special cubic Hodge integrals of the Gopakumar--Mari\~no--Vafa type [17, 28] and GUE correlators, and the conjecture… Expand

Matrix Resolvent and the Discrete KdV Hierarchy

- Physics, Mathematics
- 2019

Based on the matrix-resolvent approach, for an arbitrary solution to the discrete KdV hierarchy, we define the tau-function of the solution, and compare it with another tau-function of the solution… Expand

WKB solutions of difference equations and reconstruction by the topological recursion

- Physics, Mathematics
- 2018

The purpose of this article is to analyze the connection between Eynard–Orantin topological recursion and formal WKB solutions of a -difference equation: with . In particular, we extend the notion of… Expand

Classical Hurwitz numbers and related combinatorics

- Mathematics
- 2016

In 1891 Hurwitz [30] studied the number Hg,d of genus g ≥ 0 and degree d ≥ 1 coverings of the Riemann sphere with 2g + 2d− 2 fixed branch points and in particular found a closed formula for Hg,d for… Expand

Brezin-Gross-Witten tau function and isomonodromic deformations

- Mathematics, Physics
- 2018

The Brezin-Gross-Witten tau function is a tau function of the KdV hierarchy which arises in the weak coupling phase of the Brezin-Gross-Witten model. It falls within the family of generalized… Expand

Hermitian One-Matrix Model and KP Hierarchy

- Physics, Mathematics
- 2018

The partition functions of Hermitian one-matrix models are known to be tau-functions of the KP hierarchy. In this paper we explicitly compute the elements in Sato grassmannian these tau-functions… Expand

On the large genus asymptotics of psi-class intersection numbers

- Mathematics, Physics
- 2021

Based on an explicit formula of the generating series for the n-point psi-class intersection numbers (cf. Bertola et. al. [4]), we give a novel proof of a conjecture of Delecroix et. al. [9]… Expand

Moments of discrete orthogonal polynomial ensembles

- Mathematics, Physics
- 2020

We obtain factorial moment identities for the Charlier, Meixner and Krawtchouk orthogonal polynomial ensembles. Building on earlier results by Ledoux [Elect. J. Probab. 10, (2005)], we find… Expand

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