By Henri Epstein
By Maxim Kontsevich
Appears in collection : Combinatorics and Arithmetic for Physics
In this seminar we study the constructive loop vertex expansion for stable matrix models with (single trace) interactions of arbitrarily high even order in the Hermitian and real symmetric cases. It relies on a new and simpler method which can also be applied in the previously treated complex case. We prove analyticity in the coupling constant of the free energy for such models in a domain uniform in the size of the matrix.