You are cordially invited to the Analysis Seminar organized by the Department of Mathematics.<\/p>\n
Speaker: Yusuf \u0130sa Dural (Bilkent)<\/p>\n
\u201cThreshold Phenomena and the Kahn-Kalai Conjecture\u201d<\/p>\n
Abstract: In many random discrete structures, one observes a striking threshold phenomenon: as a model parameter passes a critical value, the behavior of the system changes abruptly. For example, in the Erd\u0151s\u2013R\u00e9nyi random graph G(n,p), when the edge probability p crosses an appropriate threshold, an event that was previously very unlikely suddenly becomes highly probable, such as the appearance of a triangle or of a Hamiltonian cycle.
\nA central question in this area is how to estimate such critical probabilities in general. The Kahn\u2013Kalai conjecture gave a remarkably general prediction, asserting that the threshold of a family of sets can be controlled, up to a logarithmic factor, by its expectation threshold.
\nThis conjecture was proved by Jinyoung Park and Huy Tuan Pham in 2022.
\nTwo years later, Phuc Tran and Van Vu found a much shorter proof. In this talk, I will introduce threshold phenomena and present a proof of the Kahn\u2013Kalai conjecture following the argument of Tran and Vu.
\n(This is a presentation of a senior project supervised by G\u00f6khan Y\u0131ld\u0131r\u0131m.)<\/p>\n
Date: May 5, Tuesday
\nTime: 14:00-15:00,
\nPlace: SA141<\/p>\n","protected":false},"excerpt":{"rendered":"
You are cordially invited to the Analysis Seminar organized by the Department of Mathematics. Speaker: Yusuf \u0130sa Dural (Bilkent) \u201cThreshold Phenomena and the Kahn-Kalai Conjecture\u201d Abstract: In many random discrete structures, one observes a striking threshold phenomenon: as a model parameter passes a critical value, the behavior of the system [\u2026] <\/p>\n