Mean quantum percolation

Charles Bordenave, Arnab Sen, Bálint Virág

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13 Scopus citations


We study the spectrum of adjacency matrices of random graphs. We develop two techniques to lower bound the mass of the continuous part of the spectral measure or the density of states. As an application, we prove that the spectral measure of bond percolation in the twodimensional lattice contains a non-trivial continuous part in the supercritical regime. The same result holds for the limiting spectral measure of a supercritical Erd'os-Rényi graph and for the spectral measure of a unimodular random tree with at least two ends. We give examples of random graphs with purely continuous spectrum.

Original languageEnglish (US)
Pages (from-to)3679-3707
Number of pages29
JournalJournal of the European Mathematical Society
Issue number12
StatePublished - 2017

Bibliographical note

Publisher Copyright:
© European Mathematical Society 2017.


  • Continuous spectra
  • Erd'os-Rényi graph
  • Expected spectral measure
  • Sparse random graphs
  • Supercritical percolation
  • Unimodular tree


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