Bordenave, Charles and Sen, Arnab and Virág, Bálint (2017) Mean quantum percolation. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 19 (12). pp. 3679-3707. ISSN 1435-9855
|
Text
1308.3755v1.pdf Download (278kB) | Preview |
Abstract
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. © European Mathematical Society 2017.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Unimodular tree; Supercritical percolation; Sparse random graphs; Expected spectral measure; Erd'os-Rényi graph; Continuous spectra |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 12 Feb 2018 08:11 |
| Last Modified: | 12 Feb 2018 08:11 |
| URI: | http://real.mtak.hu/id/eprint/74278 |
Actions (login required)
 |
Edit Item |
