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arXiv · 1202.4104

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

L. R. G. Fontes·R. J. Gava·V. Gayrard
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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.

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L. R. G. Fontes, R. J. Gava, V. Gayrard. 2012-02-18. The K-process on a tree as a scaling limit of the GREM-like trap model. https://doi.org/10.1214/13-aap937

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