PreprintCC BY 4.0arXiv
An elementary proof of Brémont's theorem on the convergence of equilibrium measures at temperature zero
Abstract
We give an elementary proof that if f is a locally constant function on a topologically mixing subshift of finite type, then the equilibrium measures for tf converge as t→∞, a result due to Brémont. The proof shows that the limit measure assigns an algebraic number to every cylinder.
Related
- Local stability and rates of convergence to equilibrium for the Nonlinear Renewal Equation; applications to Hawkes processes
- Reversible Stratonovich perturbations for accelerating convergence to equilibrium of Langevin dynamics
- Convergence of Coordinate Ascent Variational Inference for log-concave measures via optimal transport
- Equilibrium bias and convergence in augmented primal--dual dynamics with sampled constraints
- Thermodynamic Formalism Out of Equilibrium Part II: Semi-Ruelle Operator, Conformal Measures, and Effective Expansion and Quasi-Compactness
BibTeX
@misc{jenkinson2026elementary,
title = {{An elementary proof of Brémont's theorem on the convergence of equilibrium measures at temperature zero}},
author = {Oliver Jenkinson and Mark Pollicott},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19990},
eprint = {2610.19990},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19990},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An elementary proof of Brémont's theorem on the convergence of equilibrium measures at temperature zero
AU - Oliver Jenkinson
AU - Mark Pollicott
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.19990
UR - https://arxiv.org/abs/2610.19990
AB - We give an elementary proof that if f is a locally constant function on a topologically mixing subshift of finite type, then the equilibrium measures for tf converge as t→∞, a result due to Brémont. The proof shows that the limit measure assigns an algebraic number to every cylinder.
ER -