Advances in Theoretical and Mathematical Physics
Volume 7 (2003)
Matrix Integrals and Feynman Diagrams in the Kontsevich Model
Pages: 525 – 576
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.