Annales Henri Poincaré

, Volume 16, Issue 11, pp 2465–2497 | Cite as

On Quantum Percolation in Finite Regular Graphs

  • Charles BordenaveEmail author


The aim of this paper is twofold. First, we study eigenvalues and eigenvectors of the adjacency matrix of a bond percolation graph when the base graph is finite and well approximated locally by an infinite regular graph. We relate quantitatively the empirical measure of the eigenvalues and the delocalization of the eigenvectors to the spectrum of the adjacency operator of the percolation on the infinite graph. Secondly, we prove that percolation on an infinite regular tree with degree at least three preserves the existence of an absolutely continuous spectrum if the removal probability is small enough. These two results are notably relevant for bond percolation on a uniformly sampled regular graph or a Cayley graph with large girth.


Adjacency Matrix Continuous Spectrum Random Graph Regular Graph Cayley Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Basel 2014

Authors and Affiliations

  1. 1.Institut de Mathématiques de ToulouseCNRS and University of ToulouseToulouse cedex 09France

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