Explicit estimates in the Bramson-Kalikow model

Author(s)

Gallesco, C. ^[1] ; Gallo, S. ^[2] ; Takahashi, D. Y. ^{[3, 4]}

Affiliation

^[1] Univ Estadual Campinas, Inst Matemat Estat Ciencias Computat, Dept Estat, BR-13083859 Campinas, SP - Brazil

^[2] Univ Fed Rio de Janeiro, Inst Matemat, Dept Metodos Estat, BR-21941909 Rio De Janeiro - Brazil

^[3] Princeton Univ, Dept Psychol, Princeton, NJ 08544 - USA

^[4] Princeton Univ, Inst Neurosci, Princeton, NJ 08544 - USA

• Document type: Journal article
• Source: Nonlinearity; v. 27, n. 9, p. 2281-2296, SEP 2014.
• Web of Science Citations: 2

Abstract

The aim of this paper is to explicitly compute parameters for which the Bramson-Kalikow (BK) model exhibits phase transition. The main ingredient of the proof is a simple new criterion for non-uniqueness of g-measures. We show that the existence of multiple g-measures compatible with a function g can be proved by estimating the (d) over bar -distances between some suitably chosen Markov chains. The method is optimal for the important class of binary regular attractive kernels, which includes the BK model. (AU)

• FAPESP's process: 09/09809-1 - Stochastic processes with variable length memory: Monge-Kantorovich problem, bootstrap and particle systems
• Grantee: Alexsandro Giacomo Grimbert Gallo
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 08/08171-0 - Modeling populations of neurons with multicomponent systems with variable range interactions
• Grantee: Daniel Yasumasa Takahashi
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 13/10101-9 - Localization of random walks in random environment and molecular spiders
• Grantee: Christophe Frédéric Gallesco
• Support Opportunities: Regular Research Grants