THE K-PROCESS ON A TREE AS A SCALING LIMIT OF THE GREM-LIKE TRAP MODEL

• 成果类型: Article
• 署名作者: Fontes, L. R. G.; Gava, R. J.; Gayrard, V.
• 署名单位: Universidade de Sao Paulo; Universidade Federal de Sao Carlos; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/13-AAP937
• 发表日期: 2014
• 页码: 857-897
• 关键词: random energy-model; random-walks; random-environments; glauber dynamics; complete graph; spin-glasses; CONVERGENCE; UNIVERSALITY; localization; rem

摘要

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.