Law of addition in random matrix theory

Details Law of addition in random matrix theory Law of addition in random matrix theory

1996-02-28

arxiv.org/abs/cond-mat/9602146v1

Nucl.Phys. B474 (1996) 726-744

Physics

Condensed Matter

17 pages, Latex with special macro appended, hard figs available from: mason@itp.ucsb.edu

Scientific paper

10.1016/0550-3213(96)00276-3

We discuss the problem of adding random matrices, which enable 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 Br\'ezin, Hikami, and Zee. The method used here may be applied to a broad class of problems involving random matrices.

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