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

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.

Published in at http://dx.doi.org/10.1214/07-AOP360 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• Aging on Parisi's tree
• Scaling limit for trap models on ${\mathbb{Z}}^d$
• Bouchaud's model exhibits two different aging regimes in dimension one
• Spectral characterization of aging: the rem-like trap model

Cited by in corpus (13)

• Spectrum of large random reversible Markov chains: Heavy-tailed weights on the complete graph
• On the dynamics of trap models in Z^d
• Scaling limit of the random walk among random traps on Z^d
• The K-process on a tree as a scaling limit of the GREM-like trap model
• Scaling limits and aging for asymmetric trap models on the complete graph and K-processes
• Metastable Markov chains
• Dynamical Freezing in a Spin Glass System with Logarithmic Correlations
• Universality of trap models in the ergodic time scale
• Principal eigenvalue for random walk among random traps on Z^d
• Long range trap models on Z and quasistable processes
• Elementary results on K processes with weights
• Quenched scaling limits of trap models
• GREM-like K processes on trees with infinite depth