Matrix Integrals and Feynman Diagrams in the Kontsevich Model
arXiv:math/0111082
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.
52 pages; final version
References in corpus (5)
- Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
- Combinatorial and algebro-geometric cohomology classes on the moduli spaces of curves
- Polynomial averages in the Kontsevich model
- Combinatorial Miller-Morita-Mumford classes and Witten cycles
- Cohomology of moduli spaces