Non-commutative matrix integrals and representation varieties of surface groups in a finite group

Mulase, Motohico; T. Yu, Josephine

Annales de l'Institut Fourier, Tome 55 (2005) no. 6, pp. 2161-2196.

Une nouvelle formule est établie pour l'expansion asymptotique d'une intégrale matricielle avec des valeurs dans une algèbre de von Neumann de dimension finie en terme de graphes sur les surfaces orientables ou non-orientables.

A new formula is established for the asymptotic expansion of a matrix integral with values in a finite-dimensional von Neumann algebra in terms of graphs on surfaces which are orientable or non-orientable.

Classification : 15A52, 20C05, 32G13, 81Q30
Keywords: Random matrices, non-commutative matrix integral, Feynman diagram expansion, ribbon graph, Moebius graph, von Neumann algebra, representation variety
Mot clés : matrices aléatoires, intégrale non commutative de matrice, expansion de diagramme de Feynman, graphe de ruban, graphe de Moebius, algèbre de von Neumann, variété de représentations

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