Contents Online
Advances in Theoretical and Mathematical Physics
Volume 7 (2003)
Number 3
Matrix Integrals and Feynman Diagrams in the Kontsevich Model
Pages: 525 – 576
DOI: https://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.
Published 1 January 2003