Numerical calculation of correlation properties of sparse real symmetric random matrix

Abstract

The N.N.D. or a real symmetric sparse random matrix is governed by the “coupling parameter” $\overline {\left| {V_{ij} } \right|}$.

Meaningful statistical properties of a such uniform random large matrix can be obtained from the diagonalization of a submatrix ; however, this submatrix must not be too small (function of the sparseness of the large matrix). This approch will be used in the study of vibrations levels of the ground state of polyatomic molecules like formaldehyde and glyoxal. To apply this model to molecular systems, one must check that the assumption of a uniform distribution of off diagonal elements holds.