PreprintCC BY 4.0arXiv
A Randomness Test Formalism for Neutral Measures and Beyond
Abstract
We discuss in detail Neutral Measures, which are measures which believably generate any real in Cantor space. We intuitively build up the classical notions of randomness, and show that neutral measures do exist, using the language of continuous semimeasures. Finally, we construct some specific randomness tests which allow us to enforce de- sirable properties on neutral measures. As an application, we show the existence of Gibbs measures for a large class of finite range Hamilto- nians on lattice models, and establish their relationship with neutral measures.
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BibTeX
@misc{canel2026randomness,
title = {{A Randomness Test Formalism for Neutral Measures and Beyond}},
author = {Jacob Canel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28742},
eprint = {2609.28742},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28742},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Randomness Test Formalism for Neutral Measures and Beyond
AU - Jacob Canel
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28742
UR - https://arxiv.org/abs/2609.28742
AB - We discuss in detail Neutral Measures, which are measures which believably generate any real in Cantor space. We intuitively build up the classical notions of randomness, and show that neutral measures do exist, using the language of continuous semimeasures. Finally, we construct some specific randomness tests which allow us to enforce de- sirable properties on neutral measures. As an application, we show the existence of Gibbs measures for a large class of finite range Hamilto- nians on lattice models, and establish their relationship with neutral measures.
ER -