Phys. Rev. E 59, 4884–4888 (1999)Adding and multiplying random matrices: A generalization of Voiculescu’s formulasReceived 28 October 1998; published in the issue dated May 1999 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 formulas to the case of measures with an external field. A similar approach yields a relation of the same type for multiplication of random matrices. © 1999 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.59.4884
DOI:
10.1103/PhysRevE.59.4884
PACS:
05.40.-a, 02.50.-r
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