Structures Robust Under Randomness - Probabilistic Combinatorics and Thresholds
Explore the fascinating world of probabilistic combinatorics in this 54-minute conference talk by Huy Tuan Pham at BIMSA. Delve into the question of when substructures in large discrete systems remain robust under random subsampling. Examine key concepts such as the survival of complete substructures or "most" of a substructure during subsampling. Investigate important topics in probabilistic combinatorics, including thresholds in random graphs and hypergraphs. Learn about the Kahn-Kalai conjecture and its prediction regarding necessary and sufficient conditions for substructure survival. Discover the concept of "being not p-small" and its relevance in various contexts, including Michel Talagrand's conjectures on suprema of positive stochastic processes. Gain insights into recent developments in the field of structure robustness under randomness and explore new methods for verifying robustness conditions in practical applications.