Local Semicircle Law for Random Regular Graphs

Volume: 70, Issue: 10, Pages: 1898 - 1960
Published: Jul 31, 2017
Abstract
We consider random d ‐regular graphs on N vertices, with degree d at least (log N ) 4 . We prove that the Green's function of the adjacency matrix and the Stieltjes transform of its empirical spectral measure are well approximated by Wigner's semicircle law, down to the optimal scale given by the typical eigenvalue spacing (up to a logarithmic correction). Aside from well‐known consequences for the local eigenvalue distribution, this result...
Paper Details
Title
Local Semicircle Law for Random Regular Graphs
Published Date
Jul 31, 2017
Volume
70
Issue
10
Pages
1898 - 1960
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