K-processes, scaling limit and aging for the trap model in the complete graph

TL;DR

This paper investigates K-processes as scaling limits of the trap model on complete graphs, revealing their properties and aging behavior, which enhances understanding of complex stochastic systems with stable and unstable states.

Contribution

It introduces K-processes as a new class of Markov processes and demonstrates their emergence as scaling limits of the trap model in complete graphs, providing new insights into aging phenomena.

Findings

K-processes serve as scaling limits for the trap model.

Aging behavior is characterized within this framework.

The study links stable states with process dynamics.

Abstract

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.