Eigenvector localization in the heavy-tailed random conductance model
Probability
2018-01-18 v1 Spectral Theory
Abstract
We generalize our former localization result about the principal Dirichlet eigenvector of the i.i.d. heavy-tailed random conductance Laplacian to the first eigenvectors. We overcome the complication that the higher eigenvectors have fluctuating signs by invoking the Bauer-Fike theorem to show that the th eigenvector is close to the principal eigenvector of an auxiliary spectral problem.
Cite
@article{arxiv.1801.05684,
title = {Eigenvector localization in the heavy-tailed random conductance model},
author = {Franziska Flegel},
journal= {arXiv preprint arXiv:1801.05684},
year = {2018}
}
Comments
14 pages. Generalizes the results of article arXiv:1608.02415 to higher order eigenvectors. For better readability, we have copied the main definitions