The spectral edge of some random band matrices


We study the asymptotic distribution of the eigenvalues of random Hermitian periodic band matrices, focusing on the spectral edges. The eigenvalues close to the edges converge in distribution to the Airy point process if (and only if) the band is sufficiently wide ($W \gg N^{5/6}$). Otherwise, a different limiting distribution appears.


Sasha Sodin

School of Mathematical Sciences
Tel Aviv University
Ramav Aviv, Tel Aviv 69978