The spectral edge of some random band matrices

Details The spectral edge of some random band matrices The spectral edge of some random band matrices

2009-06-22

arxiv.org/abs/0906.4047v4

Ann. of Math. 172 (2010), No. 3, 2223-2251

Physics

Mathematical Physics

37 pp., 3 figures; minor revision; 24/6: fixed sign in Thm. 2 and added references

Scientific paper

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 >> N^{5/6}.) Otherwise, a different
limiting distribution appears.

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