2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/97827Within a general framework, we discuss the wave function statistics in the Lloyd model of Anderson localization on a one-dimensional lattice with a Cauchy distribution for the random on-site potential. We demonstrate that already in leading order in the disorder strength, there exists a hierarchy of anomalies in the probability distributions of the wave function, the conductance, and the local density of states, for every energy which corresponds to a rational ratio of wave length to the lattice constant. We also show that these distribution functions do have power-law rather then log-normal tails and do not display universal single-parameter scaling. These peculiarities persist in any model with power-law tails of the disorder distribution function.4 pages, 2 figuresDisordered Systems and Neural NetworksMesoscale and Nanoscale Physicstext