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arXiv · 2610.19990

An elementary proof of Brémont's theorem on the convergence of equilibrium measures at temperature zero

Oliver Jenkinson·Mark Pollicott
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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.

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Oliver Jenkinson, Mark Pollicott. 2026-10-14. An elementary proof of Brémont's theorem on the convergence of equilibrium measures at temperature zero. https://arxiv.org/abs/2610.19990

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