The spectral edge of some random band matrices

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Abstract

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.

Original languageEnglish
Pages (from-to)2223-2251
Number of pages29
JournalAnnals of Mathematics
Volume172
Issue number3
DOIs
StatePublished - 2010

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