Further remarks on fractional vs. expectation thresholds

TL;DR

This paper discusses the relationship between fractional and expectation thresholds in probabilistic combinatorics, providing new results that support Talagrand's conjecture by analyzing specific cases.

Contribution

It generalizes DeMarco and Kahn's method to settle additional special cases of Talagrand's conjecture on thresholds.

Findings

Support for Talagrand's conjecture in specific cases

Generalization of existing methods to new threshold cases

Enhanced understanding of fractional vs. expectation thresholds

Abstract

A conjecture of Talagrand (2010) states that the so-called expectation and fractional expectation thresholds are always within at most some constant factor from each other. In this note we generalize a method of DeMarco and Kahn and settle a few more special cases.