We study K-processes, which are Markov processes in a denumerable state space, all of whose elements are stable, with the exception of a single state, starting from which the process enters finite sets of stable states with uniform distribution. We show how these processes arise, in a particular instance, as scaling limits of the trap model in the complete graph, and subsequently derive aging results for those models in this context.
"K-processes, scaling limit and aging for the trap model in the complete graph." Ann. Probab. 36 (4) 1322 - 1358, July 2008. https://doi.org/10.1214/07-AOP360