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


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.


Regular Graph Chebyshev Polynomial Spherical Function Convolution Operator Regular Tree 
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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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