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.
Topological expansion of mixed correlations in the hermitian 2 Matrix Model and x-y symmetry of the F_g invariants
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abstract
We compute expectation values of mixed traces containing both matrices in a two matrix model, i.e. generating function for counting bicolored discrete surfaces with non uniform boundary conditions. As an application, we prove the $x-y$ symmetry of the algebraic curve invariants introduced in math-ph/0702045.
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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.