Law of addition in random matrix theory |
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| Institution: | 1. Department of Mathematics, The University of Jordan, Amman, Jordan;2. Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran;3. Department of Basic Sciences, Princess Sumaya University for Technology, Amman, Jordan;1. Department of Mathematics, Texas A&M University, College Station, TX, USA;2. School of Mathematics and Statistics, University of New South Wales, Kensington, NSW, Australia |
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| Abstract: | We discuss the problem of adding random matrices, which enables us to study Hamiltonians consisting of a deterministic term plus a random term. Using a diagrammatic approach and introducing the concept of “gluon connectedness”, we calculate the density of energy levels for a wide class of probability distributions governing the random term, thus generalizing a result obtained recently by Brézin, Hikami and Zee. The method used here may be applied to a broad class of problems involving random matrices. |
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