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On p-Spread Measures
Abstract
We study p-spread probability measures on the Boolean lattice. We show that if a family of sets A is large under the product Bernoulli-p measure, then no p-spread measure can be supported on sets that are not covered by the union of two members of A, answering the fractional version of Talagrand's discrete convexity problem. Consequently, we establish a coupling theorem between p-spread and product Bernoulli-p measures.
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BibTeX
@misc{li2026pspread,
title = {{On $p$-Spread Measures}},
author = {Chen Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.08967},
eprint = {2609.08967},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08967},
}
RIS
TY - UNPB
TI - On p-Spread Measures
AU - Chen Li
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2609.08967
UR - https://arxiv.org/abs/2609.08967
AB - We study p-spread probability measures on the Boolean lattice. We show that if a family of sets A is large under the product Bernoulli-p measure, then no p-spread measure can be supported on sets that are not covered by the union of two members of A, answering the fractional version of Talagrand's discrete convexity problem. Consequently, we establish a coupling theorem between p-spread and product Bernoulli-p measures.
ER -