Planar diagrams

Geometry of 2D topological field theories

“…polihedron). This way leads to considering matrix integrals of the form [22] Z N (t) = Z X = X expf tr(X 2 + t 1 X 4 + t 2 X 6 + : : : g dX (2:7) where the integral should be taken over the space of all N N Hermitean matrices X. Here t 1 , t 2 ... are called coupling constants.…”

Non-hermitian random matrix theory: Method of hermitian reduction

“…We pose this as an interesting problem, namely to find a useful quaternionic generalization of (1.1) for random non-hermitean matrices, and to develop the analogue of the work of Brézin et al [10] associated with it.…”

“…In the large N limit, the poles merge into a cut (or several cuts) on the real axis. Powerful theorems from the theory of analytic functions can then be brought to bear to the problem of determining G(z) [10]. All of this is well-known.…”

Topological expansion of the 2-matrix model correlation functions: diagrammatic rules for a residue formula

“…In this article, we consider "formal" random matrix integrals, which are known to be generating functions for counting some classes of discrete surfaces [7,10,21,22,34].…”

“…In the formal model, N is thus an expansion parameter, and working order by order in N enumerates only discrete surfaces of a given topology [7]. An efficient method for dealing with this formal model is to consider the Schwinger-Dyson equations, called loop equations in this context [10,33].…”