A bijective skinning procedure yields the topological recursion for maps of arbitrary topology at the level of formal generating series, with no analyticity assumptions, including stuffed maps and a combinatorial recursion kernel.
Higher Genus Correlators from the Hermitian One-Matrix Model
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abstract
We develop an iterative algorithm for the genus expansion of the hermitian $N\times N$ one-matrix model ( = the Penner model in an external field). By introducing moments of the external field, we prove that the genus $g$ contribution to the $m$-loop correlator depends only on $3g-2+m$ lower moments ($3g-2$ for the partition function). We present the explicit results for the partition function and the one-loop correlator in genus one. We compare the correlators for the hermitian one-matrix model with those at zero momenta for $c=1$ CFT and show an agreement of the one-loop correlators for genus zero.
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A bijective topological recursion for maps
A bijective skinning procedure yields the topological recursion for maps of arbitrary topology at the level of formal generating series, with no analyticity assumptions, including stuffed maps and a combinatorial recursion kernel.