A Proof of Talagrand's Creating Large Sets Conjecture
Combinatorics
2025-12-08 v2 Discrete Mathematics
Probability
Abstract
Talagrand conjectured that if a family of sets over is of large measure, then constant times of unions of sets in will cover a large portion of the power set of . This conjecture is a central open problem at the intersection of combinatorics and probability theory, and was described by Talagrand as a personal favorite. This paper provides a proof confirming this conjecture.
Cite
@article{arxiv.2511.17336,
title = {A Proof of Talagrand's Creating Large Sets Conjecture},
author = {Xuan Fang and Tianyu Wang},
journal= {arXiv preprint arXiv:2511.17336},
year = {2025}
}
Comments
This manuscript has been withdrawn by the authors. Upon further review, we have identified critical flaws in the analysis that invalidates the main conclusions presented. The authors intend to address these concerns and may submit a corrected version in the future. We apologize for any inconvenience this may have caused