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 with 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 (Dakel et al 2007 APPROX-RANDOM pp 436-48)