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

Author(s)

Fontes, L. R. G. ^[1] ; Gava, R. J. ^[2] ; Gayrard, V. ^[3]

Affiliation

^[1] Univ Sao Paulo, IME, BR-05508090 Sao Paulo - Brazil

^[2] Univ Fed Sao Carlos, CCET, BR-13565905 Sao Carlos, SP - Brazil

^[3] Aix Marseille Univ, CNRS, CMI, LAPT, F-13453 Marseille 13 - France

• Document type: Journal article
• Source: ANNALS OF APPLIED PROBABILITY; v. 24, n. 2, p. 857-897, APR 2014.
• Web of Science Citations: 2

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. (AU)

• FAPESP's process: 08/00999-0 - Scaling limits of trap models
• Grantee: Renato Jacob Gava
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 09/52379-8 - Stochastic modeling of interacting systems
• Grantee: Fabio Prates Machado
• Support Opportunities: Research Projects - Thematic Grants