# All genus correlation functions for the hermitian 1-matrix model

@inproceedings{Eynard2004AllGC, title={All genus correlation functions for the hermitian 1-matrix model}, author={Bertrand Eynard}, year={2004} }

We rewrite the loop equations of the hermitian matrix model, in a way which allows to compute all the correlation functions, to all orders in the topological $1/N^2$ expansion, as residues on an hyperelliptical curve. Those residues, can be represented diagrammaticaly as Feynmann graphs of a cubic interaction field theory on the curve.

## 263 Citations

Topological expansion of the 2-matrix model correlation functions: diagrammatic rules for a residue formula

- Mathematics
- 2005

We solve the loop equations of the hermitian 2-matrix model to all orders in the topological 1/N2 expansion, i.e. we obtain all non-mixed correlation functions, in terms of residues on an algebraic…

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- 2006

We compute the complete topological expansion of the formal hermitian two-matrix model. For this, we refine the previously formulated diagrammatic rules for computing the 1/N expansion of the…

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- 2007

We compute expectation values of mixed traces containing both matrices in a two matrix model, i.e. a generating function for counting bicolored discrete surfaces with non-uniform boundary conditions.…

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- Mathematics, Physics
- 2008

We solve the loop equations to all orders in $1/N^2$, for the Chain of Matrices matrix model (with possibly an external field coupled to the last matrix of the chain). We show that the topological…

Generation of matrix models by Ŵ-operators

- Mathematics
- 2009

We show that partition functions of various matrix models can be obtained by acting on elementary functions with exponents of operators. A number of illustrations is given, including the Gaussian…

Mixed correlation functions in the 2-matrix model, and the Bethe Ansatz

- Computer Science
- 2005

Using loop equation technics, all mixed traces correlation functions of the 2-matrix model to large N leading order are computed and it is found that, when the correlation functions are written collectively as a matrix, the loop equations are equivalent to commutation relations.

Loop equations and topological recursion for the arbitrary-β two-matrix model

- Mathematics, Physics
- 2012

A bstractWe write the loop equations for the β two-matrix model, and we propose a topological recursion algorithm to solve them, order by order in a small parameter. We find that to leading order,…

Topological Expansion in the Cubic Random Matrix Model

- Mathematics
- 2010

In this paper, we study the topological expansion in the cubic random matrix model, and we evaluate explicitly the expansion coefficients for genus 0 and 1. For genus 0 our formula coincides with the…

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- Mathematics
- 2005

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 spans…

JT gravity and the ensembles of random matrix theory

- PhysicsAdvances in Theoretical and Mathematical Physics
- 2020

We generalize the recently discovered relationship between JT gravity and double-scaled random matrix theory to the case that the boundary theory may have time-reversal symmetry and may have fermions…

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