Random matrices, nonbacktracking walks, and orthogonal polynomials
- 1 December 2007
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 48 (12) , 123503
- https://doi.org/10.1063/1.2819599
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 non-backtracking walks on a certain graph. Orthogonal polynomials with respect to the limiting spectral measure play a role in this approach.Comment: (more) minor changeKeywords
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This publication has 17 references indexed in Scilit:
- Concentration of norms and eigenvalues of random matricesJournal of Functional Analysis, 2004
- Rate of convergence in probability to the Marchenko-Pastur lawBernoulli, 2004
- Spectra of Regular Graphs and Hypergraphs and Orthogonal PolynomialsEuropean Journal of Combinatorics, 1996
- Limit of the Smallest Eigenvalue of a Large Dimensional Sample Covariance MatrixThe Annals of Probability, 1993
- Walk generating functions and spectral measures of infinite graphsLinear Algebra and its Applications, 1988
- Mean Convergence of Lagrange Interpolation. IIITransactions of the American Mathematical Society, 1984
- Spanning Trees in Regular GraphsEuropean Journal of Combinatorics, 1983
- The expected eigenvalue distribution of a large regular graphLinear Algebra and its Applications, 1981
- A Limit Theorem for the Norm of Random MatricesThe Annals of Probability, 1980
- Symmetric Random Walks on GroupsTransactions of the American Mathematical Society, 1959