Non-localization of eigenfunctions on large regular graphs
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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.
KeywordsRegular Graph Chebyshev Polynomial Spherical Function Convolution Operator Regular Tree
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