Zero Temperature Limits of Gibbs States for Almost-Additive Potentials

2013/09/30 by Godofredo Iommi, Yuki Yayama · 11 citations
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #Countable set #Ergodic theory #Fractal #Gibbs measure #Lyapunov exponent #Markov chain #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Measure (data warehouse) #Multifractal system #Physics #Potential theory #Pure mathematics #Quantum mechanics #Statistical physics #Statistics #Zero (linguistics) #math.DS

paper · pdf · doi:10.1007/s10955-014-0943-9

published in Journal of Statistical Physics 155(1), 23-46 (Springer Science+Business Media) · Changes in Sections 4 and 5 are included in this version

arxiv created 2013/10/24 · openalex publication_date 2014/02/24 · arxiv updated 2015/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

This paper is devoted to study ergodic optimisation problems for almost-additive sequences of functions (rather than a fixed potential) defined over countable Markov shifts (that is a non-compact space). Under certain assumptions we prove that any accumulation point of a family of Gibbs equilibrium measures is a maximising measure. Applications are given in the study of the joint spectral radius and to multifractal analysis of Lyapunov exponent of non-conformal maps.

Citations

• Ergodic optimization, zero temperature limits and the max-plus algebra
• On the Zero-Temperature Limit of Gibbs States
• Almost-additive thermodynamic formalism for countable Markov shifts
• Lyapunov exponents for products of matrices and multifractal analysis. Part II: General matrices