Eigenvector Localization for Random Band Matrices with Power Law Band Width
By Jeffrey Schenker. 2008
143 citations recorded by the source corpus.
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 μ 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 μ ≤ 8 holds.
Subfields: Computational Theory and Mathematics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/f3f045fc1cbac963421412dcc5527de55be551bd
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Theory and Mathematics
In Mathematical Physics
In Statistics and Probability
Citations in the corpus
- Extremal eigenvalues and eigenvectors of deformed Wigner matrices (2013, background): “We refer to [42, 13, 16] for more details on the localization/delocalization for random band matrices.”
- Universality of Wigner random matrices: a survey of recent results (2010, unknown): “Schenker [82] but not local statistics.”
- A Dynamical Approach to Random Matrix Theory (2017, background): “For general distribution of the matrix entries, eigenstates were proved to be localized [115] for W N, and delocalization of most eigenvectors in a certain averaged sense holds for W N [50,51], improved to W N [54].”
- Delocalization and Diffusion Profile for Random Band Matrices (2012, methodology): “[33] J. Schenker, Eigenvector localization for random band matrices with power law band width, Comm. Math.”