Formal matrix integrals and combinatorics of maps
Year: 2006
Type: preprint
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.
Author: Eynard, Bertrand
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3025397158