GranMa 2011Oct 3  6, 2011Institut Henri Poincaré, Paris 

Leonid Chekhov, Steklov Math. Inst. Moscow and Concordia Univ. Montreal: Externalfield matrix model for Gaussian loop meansUsing elementary resummations, we reduce the problem of finding muiltiloop means for Gaussian model to finding the partition function of the special onematrix model with the external field of KontsevichPenner type. It is known that this model after the Miwatype change of variables becomes equivalent to the onematrix model with an arbitrary potential. What is lesser known is that, in terms of special times, it is related to reductions of moduli spaces and, in the same special times, it admits a decomposition into a pair of Kontsevich matrix models related by a canonical transformation. For the case of one loop mean (one backbone) we use the HarerZagier recursion formulas to (i) improve the recursion itself and (ii) solve it finding for example the first reduction coefficient for the moduli spaces of curves of arbitrary genus with one marked point. Go to the GranMa home page. 