High-Dimensional Procrustes Matching via Tree Counts

Xiaochun Niu, Tselil Schramm, Jiaming Xu

Suppose we observe two sets of $n$ Gaussian vectors in ${\mathbb{R}}^d$, with the promise that, after applying a permutation of $[n]$ and a rotation of ${\mathbb{R}}^d$, the two sets a…