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Maximizing Measures for Subadditive and Almost-Additive Potentials on Countable-Alphabet Subshifts
Abstract
We prove the existence of maximizing measures for subadditive and almost-additive families of upper semicontinuous, bounded-above potentials ℱ={fn}n≥1 on closed subshifts over countable alphabets. Under a coercivity condition on f1, we prove that every maximizing sequence, that is, {μk}k≥1⊂ℳσ(X) satisfying ℱ̅(μk)→β(ℱ), is uniformly tight, preventing mass from escaping to arbitrarily large symbols. As a consequence, a maximizing measure exists.
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BibTeX
@misc{freire2026maximizing,
title = {{Maximizing Measures for Subadditive and Almost-Additive Potentials on Countable-Alphabet Subshifts}},
author = {Ricardo Freire and Juliano S. Gonschorowski},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33218},
eprint = {2610.33218},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33218},
}
RIS
TY - UNPB
TI - Maximizing Measures for Subadditive and Almost-Additive Potentials on Countable-Alphabet Subshifts
AU - Ricardo Freire
AU - Juliano S. Gonschorowski
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.33218
UR - https://arxiv.org/abs/2610.33218
AB - We prove the existence of maximizing measures for subadditive and almost-additive families of upper semicontinuous, bounded-above potentials ℱ={f_n}_n≥1 on closed subshifts over countable alphabets. Under a coercivity condition on f_1, we prove that every maximizing sequence, that is, {μ_k}_k≥1⊂ℳ_σ(X) satisfying ℱ̅(μ_k)→β(ℱ), is uniformly tight, preventing mass from escaping to arbitrarily large symbols. As a consequence, a maximizing measure exists.
ER -