Random incidence matrices: spectral density at zero energy
نویسنده
چکیده
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.
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