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PreprintCC BY 4.0arXiv

A Sklar-Type Decomposition for Positive Binary Distributions and a Gibbs Interpretation

  • Yi-Yu Lin
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Abstract

We study strictly positive multivariate binary distributions by separating one-body marginals from dependence. Local positive reweighting defines a dependence nucleus, completely characterized by the higher-order Walsh log-linear coefficients JS, |S|≥2. Any such nucleus and any strictly positive one-body marginals determine a unique joint distribution. In finite-spin Gibbs systems, these coefficients are the many-body interaction couplings.

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Cite

BibTeXRIS
BibTeX
@misc{lin2026sklartype,
  title = {{A Sklar-Type Decomposition for Positive Binary Distributions and a Gibbs Interpretation}},
  author = {Yi-Yu Lin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12805},
  eprint = {2610.12805},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12805},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Sklar-Type Decomposition for Positive Binary Distributions and a Gibbs Interpretation
AU  - Yi-Yu Lin
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.12805
UR  - https://arxiv.org/abs/2610.12805
AB  - We study strictly positive multivariate binary distributions by separating one-body marginals from dependence. Local positive reweighting defines a dependence nucleus, completely characterized by the higher-order Walsh log-linear coefficients J_S, |S|≥2. Any such nucleus and any strictly positive one-body marginals determine a unique joint distribution. In finite-spin Gibbs systems, these coefficients are the many-body interaction couplings.
ER  -