Non-localization of eigenfunctions on large regular graphs

Shimon Brooks*, Elon Lindenstrauss

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

48 Scopus citations

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.

Original languageAmerican English
Pages (from-to)1-14
Number of pages14
JournalIsrael Journal of Mathematics
Volume193
Issue number1
DOIs
StatePublished - Jan 2013

Bibliographical note

Funding Information:
∗ E.L. was supported in part by NSF grants DMS-0554345 and DMS-0800345, and ISF grant 983/09. Received December 16, 2009 and in revised form October 7, 2010

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