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- W2968578418 abstract "Abstract A fundamental question in random matrix theory is to quantify the optimal rate of convergence to universal laws. We take up this problem for the Laguerre β ensemble, characterized by the Dyson parameter β, and the Laguerre weight , in the hard edge limit. The latter relates to the eigenvalues in the vicinity of the origin in the scaled variable . Previous work has established the corresponding functional form of various statistical quantities—for example, the distribution of the smallest eigenvalue, provided that . We show, using the theory of multidimensional hypergeometric functions based on Jack polynomials, that with the modified hard edge scaling , the rate of convergence to the limiting distribution is , which is optimal. In the case , general the explicit functional form of the distribution of the smallest eigenvalue at this order can be computed, as it can for and general . An iterative scheme is presented to numerically approximate the functional form for general ." @default.
- W2968578418 created "2019-08-22" @default.
- W2968578418 creator A5019351501 @default.
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- W2968578418 date "2019-08-15" @default.
- W2968578418 modified "2023-10-16" @default.
- W2968578418 title "Finite‐size corrections at the hard edge for the Laguerre β ensemble" @default.
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- W2968578418 doi "https://doi.org/10.1111/sapm.12279" @default.
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