Random incidence matrices: spectral density at zero energy

Preprint
Publisher Website
Google Scholar
  • 29 June 2000
Abstract
We present exact results for the delta peak at zero energy in the spectral density of the random graph incidence matrix model as a function of the average connectivity. We give an analytic expression for the height of this peak, and a detailed description of the localized eigenvectors. Their total contribution to the peak is given. This allows to study analytically a delocalization and a relocalization transition for average connectivities 1.421529... and 3.154995.... We propose an explanation for the spectral singularity at average connectivity e=2.718281... by relating our problem to another enumerative problem in random graph theory, the minimal vertex cover problem.

This publication has 0 references indexed in Scilit: