Non-localization of eigenfunctions on large regular graphs

Shimon Brooks, Elon Lindenstrauss

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 languageEnglish
Pages (from-to)1-14
Number of pages14
JournalIsrael Journal of Mathematics
Volume193
Issue number1
DOIs
StatePublished - Jan 2013
Externally publishedYes

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

Funding

∗ 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

FundersFunder number
National Science FoundationDMS-0554345, DMS-0800345, 1101596
Directorate for Mathematical and Physical Sciences0800345, 0554345
Iowa Science Foundation983/09

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