The top eigenvalue of the random Toeplitz matrix and the Sine kernel

Details The top eigenvalue of the random Toeplitz matrix and the Sine kernel The top eigenvalue of the random Toeplitz matrix and the Sine kernel

2011-09-26

arxiv.org/abs/1109.5494v1

Mathematics

Probability

29 pages, no figure

Scientific paper

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 $2 \to 4$
operator norm of the Sine kernel.

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