Berry’s random wave conjecture

Establish whether eigenfunctions of classically chaotic systems behave like Gaussian random fields in the high-energy limit.

Background

The paper invokes Berry’s random wave conjecture as the broader conceptual context for studying eigenvectors of random regular graphs. The conjecture predicts Gaussian random-field behavior for high-energy eigenfunctions of classically chaotic systems. Because random regular graphs share characteristics associated with chaotic systems, including strong expansion and eigenvector delocalization, the paper presents convergence of edge eigenvectors to Gaussian waves as a graph-theoretic analogue of this conjectural phenomenon.