机器学习与数据科学博士生系列论坛（第五十一期）—— New Perspective of Expectation Thresholds and Kahn-Kalai Conjecture

摘要：
Thresholds have been a central subject in the study of random discrete structures since its initiation by Erdös and Rényi, the study of which has flourished in random graph theory, computer science and statistical physics. In order to study the actual order of thresholds of some specific properties in random graphs, Kahn and Kalai raised a key conjecture to predict the general bound of expectation thresholds, which has been proved by Park and Pham recently in an elegant way. Looking forward to the future open questions about thresholds, we illustrate the outstanding perspective which Park and Pham take in their proof and view the derivative ideas of other important results about thresholds in recent years.