Journal article

Schwinger-Dyson and loop equations for a product of square Ginibre random matrices

Stephane Dartois, Peter J Forrester

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | IOP PUBLISHING LTD | Published : 2020

Abstract

In this paper, we study the product of two complex Ginibre matrices and the loop equations satisfied by their resolvents (i.e. the Stieltjes transform of the correlation functions). We obtain using Schwinger-Dyson equation (SDE) techniques the general loop equations satisfied by the resolvents. In order to deal with the product structure of the random matrix of interest, we consider SDEs involving the integral of higher derivatives. One of the advantage of this technique is that it bypasses the reformulation of the problem in terms of singular values. As a byproduct of this study we obtain the large N limit of the Stieltjes transform of the 2-point correlation function, as well as the first ..

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University of Melbourne Researchers

Grants

Awarded by Australian Research Council


Funding Acknowledgements

SD would like to thank Valentin Bonzom, Alexandr Garbali, Jesper Ipsen and Paul Zinn-Justin for useful discussions and technical help related to this work as well as for references. This work was supported by the Australian Research Council Grant DP170102028.