Eigenvector localization for random band matrices with power law band width

Details Eigenvector localization for random band matrices with power law band width Eigenvector localization for random band matrices with power law band width

2008-09-25

arxiv.org/abs/0809.4405v2

Comm. Math. Phys. 290 (2009), 1065-1097

Physics

Mathematical Physics

30 pages; corrected typos

Scientific paper

10.1007/s00220-009-0798-0

It is shown that certain ensembles of random matrices with entries that vanish outside a band around the diagonal satisfy a localization condition on the resolvent which guarantees that eigenvectors have strong overlap with a vanishing fraction of standard basis vectors, provided the band width $W$ raised to a power $\mu$ remains smaller than the matrix size $N$. For a Gaussian band ensemble, with matrix elements given by i.i.d. centered Gaussians within a band of width $W$, the estimate $\mu \le 8$ holds.

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