Non-localization of eigenfunctions on large regular graphs

Shimon Brooks; Elon Lindenstrauss

doi:10.1007/s11856-012-0096-y

Non-localization of eigenfunctions on large regular graphs

Shimon Brooks, Elon Lindenstrauss

Research output: Contribution to journal › Article › peer-review

50 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 language	English
Pages (from-to)	1-14
Number of pages	14
Journal	Israel Journal of Mathematics
Volume	193
Issue number	1
DOIs	https://doi.org/10.1007/s11856-012-0096-y
State	Published - Jan 2013
Externally published	Yes

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

Funders	Funder number
National Science Foundation	DMS-0554345, DMS-0800345, 1101596
Directorate for Mathematical and Physical Sciences	0800345, 0554345
Iowa Science Foundation	983/09

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10.1007/s11856-012-0096-y

Cite this

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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.",

author = "Shimon Brooks and Elon Lindenstrauss",

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Non-localization of eigenfunctions on large regular graphs

Abstract

Bibliographical note

Funding

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