Permutations with few inversions are locally uniform
David Bevan · Strathprints: The University of Strathclyde institutional repository (University of Strathclyde) · 2019
We prove that permutations with few inversions exhibit a local-global dichotomy in the following sense. Suppose ${\boldsymbolσ}$ is a permutation chosen uniformly at random from the set of all permutations of $[n]$ with exactly $m=m(n)\ll n^2$ inversions. If $i