2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/183758We present a simple yet rigorous approach to the determination of the spectral dimension of random trees, based on the study of the massless limit of the Gaussian model on such trees. As a byproduct, we obtain evidence in favor of a new scaling hypothesis for the Gaussian model on generic bounded graphs and in favor of a previously conjectured exact relation between spectral and connectivity dimensions on more general tree-like structures.14 pages, 2 eps figures, revtex4. Revised version: changes in section IVCondensed MatterHigh Energy Physics - Theorytext