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 |
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Pages (from-to) | 1-14 |
Number of pages | 14 |
Journal | Israel Journal of Mathematics |
Volume | 193 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2013 |
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