Random linear extensions of posets

Linear extensions of a poset $(X, \prec)$ of size $n$ are increasing bijections from $X$ to $\{1,…,n\}$. These linear extension generalize Young tableaux and various multi-dimensional random walks models. We will survey what is known about the asymptotic and probabilistic behavior of linear extensions and present our recent work on the subject. The talk is aimed at a general audience.