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Pressure at infinity and Large Deviations

  • Godofredo Iommi
  • Thomas Jordan
  • Anibal Velozo
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Abstract

We establish level-1 large deviation principles for continuous time suspension flows over countable Markov shifts, a class of non compact dynamical systems. Our results both quantify deviations of Birkhoff averages from their typical values and, importantly, provide a large deviation principle for orbits that at a finite time are close to escaping to infinity. To overcome the challenges posed by non compactness, we introduce the notion of topological pressure at infinity and prove a variational principle linking it to its measure theoretic counterpart. This framework allows the study of a natural class of potentials, known as strongly positive recurrent, which exhibit robust thermodynamic properties. Moreover, we show that compactly supported ergodic measures are pressure dense in this setting. Applications to pressure gaps and examples are given.

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Cite

BibTeXRIS
BibTeX
@misc{iommi2026pressure,
  title = {{Pressure at infinity and Large Deviations}},
  author = {Godofredo Iommi and Thomas Jordan and Anibal Velozo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16220},
  eprint = {2609.16220},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16220},
}
RIS
TY  - UNPB
TI  - Pressure at infinity and Large Deviations
AU  - Godofredo Iommi
AU  - Thomas Jordan
AU  - Anibal Velozo
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.16220
UR  - https://arxiv.org/abs/2609.16220
AB  - We establish level-1 large deviation principles for continuous time suspension flows over countable Markov shifts, a class of non compact dynamical systems. Our results both quantify deviations of Birkhoff averages from their typical values and, importantly, provide a large deviation principle for orbits that at a finite time are close to escaping to infinity. To overcome the challenges posed by non compactness, we introduce the notion of topological pressure at infinity and prove a variational principle linking it to its measure theoretic counterpart. This framework allows the study of a natural class of potentials, known as strongly positive recurrent, which exhibit robust thermodynamic properties. Moreover, we show that compactly supported ergodic measures are pressure dense in this setting. Applications to pressure gaps and examples are given.
ER  -