Random matrices, non-backtracking walks, and orthogonal polynomials

Sasha Sodin

Published 2007-03-13, updated 2007-10-28Version 3

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.