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- W3100688052 abstract "In a recent paper, Edelman, Guionnet and P'{e}ch'{e} conjectured a particular $n^{-1}$ correction term of the smallest eigenvalue distribution of the Laguerre unitary ensemble (LUE) of order $n$ in the hard-edge scaling limit: specifically, the derivative of the limit distribution, that is, the density, shows up in that correction term. We give a short proof by modifying the hard-edge scaling to achieve an optimal $O(n^{-2})$ rate of convergence of the smallest eigenvalue distribution. The appearance of the derivative follows then by a Taylor expansion of the less optimal, standard hard-edge scaling. We relate the $n^{-1}$ correction term further to the logarithmic derivative of the Bessel kernel Fredholm determinant in the work of Tracy and Widom." @default.
- W3100688052 created "2020-11-23" @default.
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- W3100688052 date "2016-06-01" @default.
- W3100688052 modified "2023-10-16" @default.
- W3100688052 title "A note on the expansion of the smallest eigenvalue distribution of the LUE at the hard edge" @default.
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- W3100688052 doi "https://doi.org/10.1214/15-aap1121" @default.
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