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arXiv · hep-th/0511019

Correlation Functions of Complex Matrix Models

M. C. Bergère
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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.

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M. C. Bergère. 2005-12-01. Correlation Functions of Complex Matrix Models. https://doi.org/10.1088/0305-4470%2F39%2F28%2Fs01

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