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Israel Journal of Mathematics

, Volume 193, Issue 1, pp 1–14 | Cite as

Non-localization of eigenfunctions on large regular graphs

  • Shimon BrooksEmail author
  • Elon Lindenstrauss
Article

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 L 2 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.

Keywords

Regular Graph Chebyshev Polynomial Spherical Function Convolution Operator Regular Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University Magnes Press 2012

Authors and Affiliations

  1. 1.Institute for Mathematical SciencesStony Brook UniversityStony BrookUSA
  2. 2.Institute of MathematicsThe Hebrew University of JerusalemGivat Ram, JerusalemIsrael

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