1 research outputs found
Eigenvectors of the discrete Laplacian on regular graphs - a statistical approach
In an attempt to characterize the structure of eigenvectors of random regular
graphs, we investigate the correlations between the components of the
eigenvectors associated to different vertices. In addition, we provide
numerical observations, suggesting that the eigenvectors follow a Gaussian
distribution. Following this assumption, we reconstruct some properties of the
nodal structure which were observed in numerical simulations, but were not
explained so far. We also show that some statistical properties of the nodal
pattern cannot be described in terms of a percolation model, as opposed to the
suggested correspondence for eigenvectors of 2 dimensional manifolds.Comment: 28 pages, 11 figure