Non-localization of eigenfunctions on large regular graphs

作者:Brooks Shimon*; Lindenstrauss Elon
来源:Israel Journal of Mathematics, 2013, 193(1): 1-14.
DOI:10.1007/s11856-012-0096-y

摘要

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.

  • 出版日期2013-1