The K-process on a tree as a scaling limit of the GREM-like trap model
Probability
2014-03-24 v3
Abstract
We introduce trap models on a finite volume -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 -process in an infinite -level tree. From this we deduce that the -process also is the scaling limit of the GREM-like trap model on extreme time scales under a fine tuning assumption on the volumes.
Cite
@article{arxiv.1202.4104,
title = {The K-process on a tree as a scaling limit of the GREM-like trap model},
author = {L. R. G. Fontes and R. J. Gava and V. Gayrard},
journal= {arXiv preprint arXiv:1202.4104},
year = {2014}
}
Comments
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)