The Voronoi tessellation generated from eigenvalues of complex random matrices

Abstract

The Voronoi froth generated from eigenvalues of asymmetric complex random matrices is studied by numerical simulation. It is more regular than the random Voronoi froth (RVF) generated from a Poisson process. The existence of a unique tessellation, called the random matrix Voronoi froth (RMVF), follows from the universality of the distribution of eigenvalues, which is also briefly commented on. The geometrical and topological properties of the RMVF have been characterised. An empirical and accurate distribution function is also proposed for the cell side length of a RVF. Deviations from the Aboav-Weaire law are discussed. Their magnitude may be interpreted as a measure of the departure from an equilibrium structure in the frame of the statistical crystallography theory of Rivier (1985).