Topics on chains of infinite order

• Grant number: 23/07228-9
• Support Opportunities: Regular Research Grants
• Start date: November 01, 2023
• End date: October 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Christophe Frédéric Gallesco
• Grantee: Christophe Frédéric Gallesco
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated researchers: Alexsandro Giacomo Grimbert Gallo ; Daniel Yasumasa Takahashi

Abstract

Chains of infinite order are a generalization of Markov chains, where past dependency can be unbounded. These processes constitute an important class of stochastic models that includes Markov chains, stochastic models for which there is no uniqueness of the stationary measure, and non-Gibbsian models. In this project we intend to address two problems related to chains of infinite order.In the first part of the project, we will elaborate a classification of infinite order chains (positive or null recurrence and transience) according to the properties of the Ruelle operator. We will also examine the relationship between these properties and the existence and uniqueness of the g-measure. In the second part of the project, we intend to obtain explicit parameters for phase transition in the model introduced by Hulse in 2006. (AU)