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

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

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

ASJC Scopus subject areas

General Mathematics

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10.1007/s11856-012-0096-y

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title = "Non-localization of eigenfunctions on large regular graphs",

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",

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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AB - 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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Non-localization of eigenfunctions on large regular graphs

Abstract

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