2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101982We investigate random, discrete Schrödiner operators which arise naturally in the theory of random matrices, and depend parametrically on Dyson's Coulomb gas inverse temperature $β$. They belong to the class of "critical" random Schrödiner operators with random potentials which diminish as $|x|^{-{1/2}}$. We show that as a function of $β$ their eigenstates undergo a transition from extended ($β\ge 2 $) to power-law localized ($0 < β< 2$).9 pages, 0 figuresMathematical Physics15A52;81Q10text