RANDOM MATRICES: LOCALIZATION OF THE EIGENVALUES AND THE NECESSITY OF FOUR MOMENTS
TERENCE TAO, VAN VU
Consider the eigenvalues
In this paper, we show that if the entries have vanishing third moment, then for all
\indent As a corollary, we show that the four moment condition in the Four Moment Theorem is necessary, in the sense that if one allows the fourth moment to change (while keeping the first three moments fixed), then the mean of