WIAS Preprint No. 2472, (2018)

Eigenvector localization in the heavy-tailed random conductance model


Authors

  • Flegel, Franziska

2010 Mathematics Subject Classification

  • 47B80 47A75 60K37

Keywords

  • Random conductance model, Dirichlet spectrum, eigenfunction localization, heavy tails, extreme value analysis

DOI

10.20347/WIAS.PREPRINT.2472

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 k eigenvectors. We overcome the complication that the higher eigenvectors have fluctuating signs by invoking the Bauer-Fike theorem to show that the kth eigenvector is close to the principal eigenvector of an auxiliary spectral problem.

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