Luke Turvey

Permutations from ranking independent random variables

Let $X_1,\ldots,X_n$ be almost surely distinct independent real-valued random variables. Let $\sigma$ be the random permutation of $\{1,\ldots,n\}$ such that $X_{\sigma(1)}<X_{\sigma(2)}<\cdots<X_{\sigma(n)}$. We show that the set of laws of $\sigma$, as the laws of $X_1,\ldots,X_n$ vary, has semialgebraic dimension \[...