Geodesic
Mean quantum percolation
Journal of the European Mathematical Society, Tome 19 (2017) no. 12, pp. 3679-3707 Cet article a éte moissonné depuis la source EMS Press

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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 two-dimensional lattice contains a non-trivial continuous part in the supercritical regime. The same result holds for the limiting spectral measure of a supercritical Erdős–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.
DOI : 10.4171/jems/750
Classification : 60-XX
Keywords: Expected spectral measure, continuous spectra, sparse random graphs, supercritical percolation, unimodular tree, Erdős–Rényi graph 
@article{JEMS_2017_19_12_a3,
     author = {Charles Bordenave and Arnab Sen and B\'alint Vir\'ag},
     title = {Mean quantum percolation},
     journal = {Journal of the European Mathematical Society},
     pages = {3679--3707},
     year = {2017},
     volume = {19},
     number = {12},
     doi = {10.4171/jems/750},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/750/}
}
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Charles Bordenave; Arnab Sen; Bálint Virág. Mean quantum percolation. Journal of the European Mathematical Society, Tome 19 (2017) no. 12, pp. 3679-3707. doi: 10.4171/jems/750

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