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Citations From References: 2 From Reviews: 0 Previous Up Next MR3101841 (Review) 60B20 Tao, Terence [Tao, Terence C.] (1-UCLA) The asymptotic distribution of a single eigenvalue gap of a Wigner matrix. (English summary) Probab. Theory Related Fields 157 (2013), no. 1-2, 81–106. Let Mn be a Hermitian n × n Wigner matrix and (λi (Mn ))ni=1 the collection of its nondecreasing eigenvalues. Let ρSC stand for the density of the Wigner distribution and ui be the real where the distribution function of ρSC equals i/n. If n ≤ i ≤ (1 − )n for some > 0 then the author proves under certain conditions on moments that the rescaled i-th single eigenvalue gap λi+1 (Mn ) − λi (Mn ) √ (1/ nρSC (ui )) converges in distribution as n → ∞ to the so-called Gaudin-Mehta distribution. The proof is written for the GUE and the result extends to Wigner matrices by the Four Nizar Demni Moment Theorem due to the author and Van Vu. References 1. 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