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Статья

Colored graphs and matrix integrals

Proceedings of the Steklov Institute of Mathematics. 2009. Vol. 264. No. 1. P. 2-19.
We discuss applications of generating functions for colored graphs to asymptoticexpansions of matrix integrals. The described technique provides an asymptotic expansionof the Kontsevich integral. We prove that this expansion is a refinement of the Kontsevichexpansion, which is the sum over the set of classes of isomorphic ribbon graphs. This yields aproof of Kontsevich’s results that is independent of the Feynman graph technique.