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.
Formal matrix integrals and combinatorics of maps
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abstract
This article is a short review on the relationship between convergent matrix integrals, formal matrix integrals, and combinatorics of maps. We briefly summarize results developed over the last 30 years, as well as more recent discoveries. We recall that formal matrix integrals are identical to combinatorial generating functions for maps, and that formal matrix integrals are in general very different from convergent matrix integrals. Finally, we give a list of the classical matrix models which have played an important role in physics in the past decades. Some of them are now well understood, some are still difficult challenges.
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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.