2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137765We introduce a model of a randomly growing interface in multidimensional Euclidean space. The growth model incorporates a random order model as an ingredient of its graphical construction, in a way that replicates the connection between the planar increasing sequences model and the one-dimensional Hammersley process. We prove a hydrodynamic limit for the height process, and a limit which says that certain perturbations of the random surface follow the characteristics of the macroscopic equation. By virtue of the space-time Poissonian construction, we know the macroscopic velocity function explicitly up to a constant factor.Published at http://dx.doi.org/10.1214/074921707000000373 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)Probability60K35 (Primary); 82C22 (Secondary)text