Graphs and Matroids - Thinula De Silva

Title:Non-uniform Kahn-Kalai: the fractional version, the dual and its power in capturing “thresholds"

Abstract:There have been several advancements in the study of thresholds in recent years, including the groundbreaking proof of the Kahn-Kalai conjecture by Park and Pham. B. Park and Vondrák also later extended this work in the non-uniform setting (where we allow different edges to have different probabilities, unlike G(n, p)). In many concrete applications of determining thresholds in G(n, p), “spread" is used to prove the 1-statement. In this talk, we extend the notion of “spread" in the non-uniform setting to test its power in capturing the “threshold". This talk is based on joint work with Jane Gao.