## The Annals of Applied Probability

### 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.

#### Article information

Source
Ann. Appl. Probab., Volume 24, Number 2 (2014), 857-897.

Dates
First available in Project Euclid: 10 March 2014

https://projecteuclid.org/euclid.aoap/1394465373

Digital Object Identifier
doi:10.1214/13-AAP937

Mathematical Reviews number (MathSciNet)
MR3178499

Zentralblatt MATH identifier
1302.60133

#### Citation

Fontes, L. R. G.; Gava, R. J.; Gayrard, V. The K -process on a tree as a scaling limit of the GREM-like trap model. Ann. Appl. Probab. 24 (2014), no. 2, 857--897. doi:10.1214/13-AAP937. https://projecteuclid.org/euclid.aoap/1394465373

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