2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/226283We consider symmetric trap models in the d-dimensional hypercube whose ordered mean waiting times, seen as weights of a measure in the natural numbers, converge to a finite measure as d diverges, and show that the models suitably represented converge to a K process as d diverges. We then apply this result to get K processes as the scaling limits of the REM-like trap model and the Random Hopping Times dynamics for the Random Energy Model in the hypercube in time scales corresponding to the ergodic regime for these dynamics.11 pages; 2 figures; mistake in (3.1) of previous version correctedProbability60K35, 60K37, 82C44text