Correlation Functions of Complex Matrix Models

Abstract

For a restricted class of potentials (harmonic+Gaussian potentials), we express the resolvent integral for the correlation functions of simple traces of powers of complex matrices of size $N$, in term of a determinant; this determinant is function of four kernels constructed from the orthogonal polynomials corresponding to the potential and from their Cauchy transform. The correlation functions are a sum of expressions attached to a set of fully packed oriented loops configurations; for rotational invariant systems, explicit expressions can be written for each configuration and more specifically for the Gaussian potential, we obtain the large $N$ expansion ('t Hooft expansion) and the so-called BMN limit.

latex BMN.tex, 7 files, 6 figures, 30 pages (v2 for spelling mistake and added reference) [http://www-spht.cea.fr/articles/T05/174]

References in corpus (1)

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

Cited by in corpus (3)

• Weighted Hurwitz numbers and topological recursion
• 1/2-BPS Correlators as c=1 S-matrix
• Surprising Pfaffian factorizations in Random Matrix Theory with Dyson index $\beta =2$