Random matrices, nonbacktracking walks, and orthogonal polynomials

doi:10.1063/1.2819599

beta

Random matrices, nonbacktracking walks, and orthogonal polynomials

S. Sodin

Mar 13, 2007

Citations

Journal

Journal of Mathematical Physics

Full text

Semantic Scholar

Key Takeaway

Key Takeaway: This paper explores how nonbacktracking walks on a graph can be used to prove Wigner's law and the Marchenko-Pastur law in random matrix theory.

Abstract

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 nonbacktracking walks on a certain graph. Orthogonal polynomials with respect to the limiting spectral measure play a role in this approach.

Text copied to clipboard

copied to clipboard