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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Volume 264, Pages 8–24 (Mi tm810)  
Colored Graphs and Matrix Integrals

I. V. Artamkin

Faculty of Mathematics, State University – Higher School of Economics, Moscow, Russia
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Abstract: We discuss applications of generating functions for colored graphs to asymptotic expansions of matrix integrals. The described technique provides an asymptotic expansion of the Kontsevich integral. We prove that this expansion is a refinement of the Kontsevich expansion, which is the sum over the set of classes of isomorphic ribbon graphs. This yields a proof of Kontsevich's results that is independent of the Feynman graph technique.
Received in August 2008
English version:
Proceedings of the Steklov Institute of Mathematics, 2009, Volume 264, Pages 2–17
DOI: https://doi.org/10.1134/S0081543809010027
Bibliographic databases:
UDC: 512.7
Language: Russian
Citation: I. V. Artamkin, “Colored Graphs and Matrix Integrals”, Multidimensional algebraic geometry, Collected papers. Dedicated to the Memory of Vasilii Alekseevich Iskovskikh, Corresponding Member of the Russian Academy of Sciences, Trudy Mat. Inst. Steklova, 264, MAIK Nauka/Interperiodica, Moscow, 2009, 8–24; Proc. Steklov Inst. Math., 264 (2009), 2–17
Citation in format AMSBIB
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\publ MAIK Nauka/Interperiodica
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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