A Proof of Talagrand's Creating Large Sets Conjecture
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909945395412992 |
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| author | Fang, Xuan Wang, Tianyu |
| author_facet | Fang, Xuan Wang, Tianyu |
| contents | Talagrand conjectured that if a family of sets $\mathcal{F}$ over $X = \{ 1,2,\cdots, N \}$ is of large measure, then constant times of unions of sets in $\mathcal{F}$ will cover a large portion of the power set of $X$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17336 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Proof of Talagrand's Creating Large Sets Conjecture Fang, Xuan Wang, Tianyu Combinatorics Discrete Mathematics Probability Talagrand conjectured that if a family of sets $\mathcal{F}$ over $X = \{ 1,2,\cdots, N \}$ is of large measure, then constant times of unions of sets in $\mathcal{F}$ will cover a large portion of the power set of $X$. 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. |
| title | A Proof of Talagrand's Creating Large Sets Conjecture |
| topic | Combinatorics Discrete Mathematics Probability |
| url | https://arxiv.org/abs/2511.17336 |