A Proof of the Kahn-Kalai Conjecture

Jinyoung Park

Thresholds for increasing properties of random structures are a central concern in probabilistic combinatorics and related areas.  In 2006, Kahn and Kalai conjectured that for any nontrivial increasing property on a finite set, its threshold is never far from its "expectation-threshold," which is a natural (and often easy to calculate) lower bound on the threshold. In the first talk, I will introduce the Kahn-Kalai Conjecture with some motivating examples and then briefly talk about the recent resolution of the Kahn-Kalai Conjecture due to Huy Pham and myself. In the second talk, I will discuss our proof of the conjecture in details.

https://www.ias.edu/video/proof-kahn-kalai-conjecture