%0 Journal Article
%T The K-process on a tree as a scaling limit of the GREM-like trap model
%+ Instituto de Matemática e Estatística (IME)
%+ Institut de Mathématiques de Marseille (I2M)
%A Fontes, L. R. G.
%A Gava, R. J.
%A Gayrard, V.
%Z 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)
%< avec comité de lecture
%@ 1050-5164
%J The Annals of Applied Probability
%I Institute of Mathematical Statistics (IMS)
%V 24
%N 2
%8 2014-04
%D 2014
%Z 1202.4104
%R 10.1214/13-AAP937
%Z Mathematics [math]
%Z Physics [physics]/Mathematical Physics [math-ph]Journal articles
%X 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.
%G English
%L hal-01257154
%U https://hal.science/hal-01257154
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ INSMI
%~ I2M
%~ I2M-2014-
%~ TDS-MACS