Random matrices, non-backtracking walks, and orthogonal polynomials

Details Random matrices, non-backtracking walks, and orthogonal polynomials Random matrices, non-backtracking walks, and orthogonal polynomials

2007-03-13

arxiv.org/abs/math-ph/0703043v3

J. Math. Phys. 48 (2007), no. 12

Physics

Mathematical Physics

(more) minor changes

Scientific paper

10.1063/1.2819599

Several well-known results from the random matrix theory, such as Wigner's
law and the Marchenko--Pastur law, can be interpreted (and proved) in terms of
non-backtracking walks on a certain graph. Orthogonal polynomials with respect
to the limiting spectral measure play a role in this approach.

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