2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/117841We show that certain Markov jump processes associated to crystal growth models are positive recurrent when the parameters satisfy a rather natural condition.Published at http://dx.doi.org/10.1214/105051606000000079 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)Probability60J20 (Primary) 60G55, 60K25, 60J10, 80A30 (Secondary)text