The K-process on a tree as a scaling limit of the GREM-like trap model

Abstract

We introduce trap models on a finite volume $k$-level tree as a class of Markov jump processes with state space the leaves of that tree. They serve to describe the GREM-like trap model of Sasaki and Nemoto. Under suitable conditions on the parameters of the trap model, we establish its infinite volume limit, given by what we call a $K$-process in an infinite $k$-level tree. From this we deduce that the $K$-process also is the scaling limit of the GREM-like trap model on extreme time scales under a fine tuning assumption on the volumes.

Published in at http://dx.doi.org/10.1214/13-AAP937 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• Spectral characterization of aging: the rem-like trap model
• K-processes, scaling limit and aging for the trap model in the complete graph
• Convergence to extremal processes in random environments and extremal ageing in SK models
• Scaling limits and aging for asymmetric trap models on the complete graph and K-processes

Cited by in corpus (1)

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