Adding and multiplying random matrices: a generalization of Voiculescu's formulas.
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.
Zinn-Justin
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New High Energy Theory Center, 126 Frelinghuysen Road, Piscataway, New Jersey 08854-8019, USA. pzinn@physics.rutgers.edu