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. 

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References

SHOWING 1-10 OF 37 REFERENCES
The Extended Toda Hierarchy
We present the Lax pair formalism for certain extension of the continuous limit of the classical Toda lattice hierarchy, provide a well defined notion of tau function for its solutions, and give anExpand
Virasoro Symmetries of the Extended Toda Hierarchy
We prove that the extended Toda hierarchy of [1] admits a nonabelian Lie algebra of infinitesimal symmetries isomorphic to half of the Virasoro algebra. The generators Lm, m≥−1 of the Lie algebra actExpand
Exact 2-point function in Hermitian matrix model
J. Harer and D. Zagier have found a strikingly simple generating function (1, 2) for exact (all-genera) 1-point correlators in the Gaussian Hermitian matrix model. In this paper we generalize theirExpand
Simple Lie Algebras, Drinfeld–Sokolov Hierarchies, and Multi-Point Correlation Functions
For a simple Lie algebra $\mathfrak{g}$, we derive a simple algorithm for computing logarithmic derivatives of tau-functions of Drinfeld--Sokolov hierarchy of $\mathfrak{g}$-type in terms ofExpand
Correlation functions of the KdV hierarchy and applications to intersection numbers over M¯g,n
We derive an explicit generating function of correlations functions of an arbitrary tau-function of the KdV hierarchy. In particular applications, our formulation gives closed formulae of a new typeExpand
D-particles, matrix integrals and KP hierarchy
Abstract We study the regularized correlation functions of the light-like coordinate operators in the reduction to zero dimensions of the matrix model describing D-particles in four dimensions. WeExpand
Matrix models of two-dimensional gravity and Toda theory
Abstract Recurrent relations for orthogonal polynomials, arising in the study of the one-matrix model of two-dimensional gravity, are shown to be equivalent to the equations of the Toda-chainExpand
Random Matrices, Graphical Enumeration and the Continuum Limit of Toda Lattices
In this paper we derive analytic characterizations for and explicit evaluations of the coefficients of the matrix integral genus expansion. The expansion itself arises from the large N asymptoticExpand
The Continuum Limit of Toda Lattices for Random Matrices with Odd Weights
This paper is concerned with the asymptotic behavior of the free energy for a class of Hermitean random matrix models, with odd degree polynomial potential, in the large N limit. It continues anExpand
Hermitian matrix model free energy: Feynman graph technique for all genera
We present the diagrammatic technique for calculating the free energy of the Hermitian one-matrix model to all orders of 1/N expansion in the case where the limiting eigenvalue distribution spansExpand
...
1
2
3
4
...