PreprintCC BY 4.0arXiv
Large deviations for observables with logarithmic singularity and differentiability of the pressure function
Abstract
We show that logarithmic observables of form ϕ(x)=log(|x−b|) on the doubling map T have exponential large deviations with respect to the invariant measure if b is preperiodic but not periodic with respect to T giving a counterpart to the known result of strictly stretched exponential large deviations in the case that b is periodic. These results are established by showing that the topological pressure function developed for unbounded observables is differentiable at $0$.
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BibTeX
@misc{nicol2026large,
title = {{Large deviations for observables with logarithmic singularity and differentiability of the pressure function}},
author = {Matthew Nicol and Tanja I. Schindler},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35221},
eprint = {2610.35221},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35221},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Large deviations for observables with logarithmic singularity and differentiability of the pressure function
AU - Matthew Nicol
AU - Tanja I. Schindler
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35221
UR - https://arxiv.org/abs/2610.35221
AB - We show that logarithmic observables of form ϕ(x)=log(|x−b|) on the doubling map T have exponential large deviations with respect to the invariant measure if b is preperiodic but not periodic with respect to T giving a counterpart to the known result of strictly stretched exponential large deviations in the case that b is periodic. These results are established by showing that the topological pressure function developed for unbounded observables is differentiable at $0$.
ER -