Non-localization of eigenfunctions on large regular graphs

2009/12/16 by Shimon Brooks, Elon Lindenstrauss, Brooks, Shimon +1 · 1 citation
Mathematics · #advanced mathematical theories #Graph theory and applications #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.0912.3239

Abstract

We give a delocalization estimate for eigenfunctions of the discrete Laplacian on large d+1-regular graphs, showing that any subset of the graph supporting ε of the L² mass of an eigenfunction must be large. For graphs satisfying a mild girth-like condition, this bound will be exponential in the size of the graph.

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