Large deviation principle for Gibbs-equilibrium states on contable shifts at zero temperature.

Author(s)

Edgardo Enrique Perez Reyes

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI)
• Defense date: 2015-03-13

Examining board members

Renaud Daniel Jacques Leplaideur; Albert Meads Fisher; Ricardo dos Santos Freire Junior; Artur Oscar Lopes; Ali Messaoudi

• Advisor: Rodrigo Bissacot Proença; Renaud Daniel Jacques Leplaideur

Abstract

Let $\\Sigma_(\\mathbb)$ be a topologically mixing countable Markov shift with the BIP property over the alphabet $\\mathbb$ and a potential $f: \\Sigma_(\\mathbb) ightarrow \\mathbb$ with summable variation and finite pressure. Under suitable hypotheses, we prove the existence of a large deviation principle for the family of Gibbs states $(\\mu_{\\beta})_{\\beta > 0}$ where each $\\mu_{\\beta}$ is the Gibbs measure associated to the potential $\\beta f$. For do this we generalize some theorems from finite to countable Markov shifts in Ergodic Optimization. This result generalizes the same principle in the case of topologically mixing subshifts over a finite alphabet previously proved by A. Baraviera, A. Lopes and P. Thieullen. (AU)

• FAPESP's process: 12/06368-7 - Large deviations principles for Gibbs-Equilibrium measures on countable Markov shifts at zero temperature
• Grantee: Edgardo Enrique Perez Reyes
• Support Opportunities: Scholarships in Brazil - Doctorate