An elementary proof of Brémont's theorem on the convergence of equilibrium measures at temperature zero
Year: 2026
Type: preprint
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 $t\to\infty$, a result due to Brémont. The proof shows that the limit measure assigns an algebraic number to every cylinder.
Source: arXiv (Cornell University)
Authors: Jenkinson, Oliver, Pollicott, Mark
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222168067