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# Advances in Theoretical and Mathematical Physics

## Volume 7 (2003)

### Number 3

### Matrix Integrals and Feynman Diagrams in the Kontsevich Model

Pages: 525 – 576

DOI: http://dx.doi.org/10.4310/ATMP.2003.v7.n3.a6

#### Authors

#### 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.