Work

A Bayesian Proof of the Spread Lemma

Year: 2025

Type: article

Abstract: ABSTRACT A key set‐theoretic “spread” lemma has been central to two recent celebrated results in combinatorics: the recent improvements on the sunflower conjecture by Alweiss, Lovett, Wu, and Zhang; and the proof of the fractional Kahn–Kalai conjecture by Frankston, Kahn, Narayanan, and Park. In this work, we present a new proof of the spread lemma, that—perhaps surprisingly—takes advantage of an explicit recasting of the proof in the language of Bayesian inference. We show that from this viewpoint the reasoning proceeds in a straightforward and principled probabilistic manner, leading to a truncated second moment calculation which concludes the proof.

Source: Random Structures and Algorithms

DOI: 10.1002/rsa.70008

Authors: Elchanan Mossel, Jonathan Niles‐Weed, Nike Sun, Ilias Zadik

Institutions: Massachusetts Institute of Technology, Courant Institute of Mathematical Sciences, New York University, Yale University

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,550