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The top eigenvalue of the random Toeplitz matrix and the sine kernel
Published 26 Sep 2011 in math.PR | (1109.5494v2)
Abstract: We show that the top eigenvalue of an $n\times n$ random symmetric Toeplitz matrix, scaled by $\sqrt{2n\log n}$, converges to the square of the $2\to4$ operator norm of the sine kernel.
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