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Adding and multiplying random matrices: a generalization of Voiculescu's formulae

P. Zinn-Justin
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Abstract

In this paper, we give an elementary proof of the additivity of the functional inverses of the resolvents of large $N$ random matrices, using recently developed matrix model techniques. This proof also gives a very natural generalization of these formulae to the case of measures with an external field. A similar approach yields a relation of the same type for multiplication of random matrices.

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P. Zinn-Justin. 1999-01-14. Adding and multiplying random matrices: a generalization of Voiculescu's formulae. https://doi.org/10.1103/physreve.59.4884

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