Jacobi polynomial moments and products of random matrices
| Autor: | Wolfgang Gawronski, Thorsten Neuschel, Dries Stivigny |
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| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Multivariate random variable General Mathematics FOS: Physical sciences random matrices distribution of eigenvalues Moment problem Matrix (mathematics) Classical Analysis and ODEs (math.CA) FOS: Mathematics free probability theory Circular ensemble Mathematical Physics Mathematics Random graph Applied Mathematics Probability (math.PR) Random element Raney distributions Mathematical Physics (math-ph) Algebra of random variables Algebra Circular law Mathematics - Classical Analysis and ODEs Jacobi polynomials free multiplicative convolution Random matrix Mathematics - Probability |
| Zdroj: | Proceedings of the American Mathematical Society. 144:5251-5263 |
| ISSN: | 1088-6826 0002-9939 |
| DOI: | 10.1090/proc/13153 |
| Popis: | Motivated by recent results in random matrix theory we will study the distributions arising from products of complex Gaussian random matrices and truncations of Haar distributed unitary matrices. We introduce an appropriately general class of measures and characterize them by their moments essentially given by specific Jacobi polynomials with varying parameters. Solving this moment problem requires a study of the Riemann surfaces associated to a class of algebraic equations. The connection to random matrix theory is then established using methods from free probability. ispartof: Proceedings of the American Mathematical Society vol:144 issue:12 pages:5251-5263 status: published |
| Databáze: | OpenAIRE |
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