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

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Published Article
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DOI: 10.1103/PhysRevE.59.4884
arXiv ID: math-ph/9810010
Source
arXiv
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Unknown
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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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