Publication : t05/241

Formal matrix integrals and combinatorics of maps

Eynard B. (CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)
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.
Année de publication : 2007
Revue : CRM Series Math. Phys. (2007)
Communication invitée : Random Matrices, Random Processes and Integrable Systems ; Université de Montréal, Montréal, Canada ; 2005-06-20 / 2005-07-20
Preprint : arXiv:math-ph/0611087
Langue : Anglais

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