Adding and multiplying random matrices: a generalization of Voiculescu's formulae
arXiv:math-ph/9810010 · doi:10.1103/PhysRevE.59.4884
Abstract
In this paper, we give an elementary proof of the additivity of the functional inverses of the resolvents of large 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.
11 pages, harvmac. revised x 2: refs and minor comments added
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