A Bayesian Proof of the Spread Lemma
Name
Random Struct Algorithms - 2025 - Mossel - A Bayesian Proof of the Spread Lemma.pdf
Description
Published version
Size
188.55 KB
Format
Adobe PDF
Checksum (MD5)
f41486da428b609684043c8d426080ba
Author(s)
Mossel, Elchanan
Niles‐Weed, Jonathan
Sun, Nike
Zadik, Ilias
Date Issued
June 6, 2025
Journal
Random Structures & Algorithms
Publisher
Wiley
Citation
Mossel, E., Niles-Weed, J., Sun, N. and Zadik, I. (2025), A Bayesian Proof of the Spread Lemma. Random Struct Alg, 66: e70008.
Version
Final published version
Abstract
A key set-theoretic “spread” lemma has been central to two recent celebrated results in combinatorics: the recentimprovements on the sunflower conjecture by Alweiss, Lovett, Wu, and Zhang; and the proof of the fractionalKahn–Kalai conjecture by Frankston, Kahn, Narayanan, and Park. In this work, we present a new proof of the spreadlemma, that—perhaps surprisingly—takes advantage of an explicit recasting of the proof in the language of Bayesianinference. We show that from this viewpoint the reasoning proceeds in a straightforward and principled probabilisticmanner, leading to a truncated second moment calculation which concludes the proof.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1002/rsa.70008
