Eigenvector localization in the heavy-tailed random conductance model

Franziska Flegel

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arXiv · 1801.05684

Eigenvector localization in the heavy-tailed random conductance model

Franziska Flegel

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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 $k$th eigenvector is close to the principal eigenvector of an auxiliary spectral problem.

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Franziska Flegel. 2018-01-17. Eigenvector localization in the heavy-tailed random conductance model. https://arxiv.org/abs/1801.05684

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