Non-localization of eigenfunctions on large regular graphs

Details Non-localization of eigenfunctions on large regular graphs Non-localization of eigenfunctions on large regular graphs

2009-12-16

arxiv.org/abs/0912.3239v1

Mathematics

Dynamical Systems

11 pages

Scientific paper

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 $\epsilon$ 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.

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