Random matrices, non-backtracking walks, and orthogonal polynomials
数学物理
2009-11-13 v3 math.MP
谱理论
摘要
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.
引用
@article{arxiv.math-ph/0703043,
title = {Random matrices, non-backtracking walks, and orthogonal polynomials},
author = {Sasha Sodin},
journal= {arXiv preprint arXiv:math-ph/0703043},
year = {2009}
}
备注
(more) minor changes