## A Note on the Kahn-Kalai Conjecture

Erdős–Rényi Model - a random graph model The Erdős–Rényi model in probability theory is a model for generating random graphs. There are two closely related variants of Erdős–Rényi models. In the $G(n,M)$ a graph is chosen uniformly at random from the collection of graphs which have $n$ nodes and $M$ edges. In the $G(n,p)$ model, a graph on $n$ vertices is constructed by randomly adding edges with probability $p$. We sometimes view these graphs as subsets of $\lbrace 0,1\rbrace^{\begin{pmatrix}[n] \\2 \end{pmatrix}}$, where the edges are randomly selected from the set $$\begin{pmatrix}[n] \\2\end{pmatrix} = \lbrace \lbrace a,b\rbrace \mid 1\leq a < b \leq n\rbrace....