The case of equality in BK — Draconitic Research

Abstract

We characterize the pairs of increasing events A,B for which there is equality in the BK inequality. Namely, we show that P(A∘ B)=P(A)P(B) if and only if all the configurations in A× B admit disjoint witnesses for A and B. We discuss the strengthened BK inequality, and we provide a new simplified proof of this inequality.

Cite

BibTeX RIS

BibTeX

@misc{cerf2026case,
  title = {{The case of equality in BK}},
  author = {Raphaël Cerf and Pierre Tesio},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.02272},
  eprint = {2607.02272},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.02272},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - The case of equality in BK
AU  - Raphaël Cerf
AU  - Pierre Tesio
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2607.02272
UR  - https://arxiv.org/abs/2607.02272
AB  - We characterize the pairs of increasing events A,B for which there is equality in the BK inequality. Namely, we show that P(A∘ B)=P(A)P(B) if and only if all the configurations in A× B admit disjoint witnesses for A and B. We discuss the strengthened BK inequality, and we provide a new simplified proof of this inequality.
ER  -