Extreme eigenvalues of random matrices from Jacobi ensembles
Two-term asymptotic formulæ for the probability distribution functions for the smallest eigenvalue of the Jacobi β-Ensembles are derived for matrices of large size in the régime where β > 0 is arbitrary and one of the model parameters α1 is an integer. By a straightforward transformation this lea...
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| Published in | Journal of mathematical physics Vol. 65; no. 9 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
01.09.2024
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| Online Access | Get full text |
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| Summary: | Two-term asymptotic formulæ for the probability distribution functions for the smallest eigenvalue of the Jacobi β-Ensembles are derived for matrices of large size in the régime where β > 0 is arbitrary and one of the model parameters α1 is an integer. By a straightforward transformation this leads to corresponding results for the distribution of the largest eigenvalue. The explicit expressions are given in terms of multi-variable hypergeometric functions, and it is found that the first-order corrections are proportional to the derivative of the leading order limiting distribution function. In some special cases β = 2 and/or small values of α1, explicit formulæ involving more familiar functions, such as the modified Bessel function of the first kind, are presented. |
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| ISSN: | 0022-2488 1089-7658 |
| DOI: | 10.1063/5.0199552 |