Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Li, Chen
Institution: New York University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212087038