Asymptotic behaviour and stationary distributions of locally interacting birth-and-death processes

• Grant number: 15/07712-1
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: July 24, 2015
• End date: September 12, 2015
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Anatoli Iambartsev
• Grantee: Anatoli Iambartsev
• Visiting researcher: Vadim Shcherbakov
• Visiting researcher institution: Lomonosov Moscow State University (MSU), Russia
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In this project we plan to study an asymptotic behaviour and stationary distributions of Markov chains describing a system of locally interacting non-negative spins. This class of Markov chains is closely related to interacting particle systems and Gibbs modelswith non-negative spins. Invariant distributions of Markov chains form a special class of Gibbs measures on graphs and are of interest on their own. (AU)