2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101253We study a class of one-dimensional interacting particle systems with random boundaries as a microscopic model for Stefan's melting and freezing problem. We prove that under diffusive rescaling these particle systems exhibit a hydrodynamic behavior described by the solution of a Cauchy--Stefan problem.Published at http://dx.doi.org/10.1214/009117905000000701 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)Probability60K35 (Primary)text