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Matrix Integrals and Feynman Diagrams in the Kontsevich Model

Domenico Fiorenza·Riccardo Murri
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Abstract

We review some relations occurring between the combinatorial intersection theory on the moduli spaces of stable curves and the asymptotic behavior of the 't Hooft-Kontsevich matrix integrals. In particular, we give an alternative proof of the Witten-Di Francesco-Itzykson-Zuber theorem --which expresses derivatives of the partition function of intersection numbers as matrix integrals-- using techniques based on diagrammatic calculus and combinatorial relations among intersection numbers. These techniques extend to a more general interaction potential.

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Domenico Fiorenza, Riccardo Murri. 2003-12-23. Matrix Integrals and Feynman Diagrams in the Kontsevich Model. https://arxiv.org/abs/math/0111082

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