Equidistribution of points in the harmonic ensemble for the Wasserstein distance
Abstract
Abstract We study the asymptotics of the expected Wasserstein distance between the empirical measure of a point process and the background volume form. The main determinantal point process studied is the harmonic ensemble, where we get the optimal rate of convergence for homogeneous manifolds of dimension , and for two‐point homogeneous manifolds. We also discuss some variations of this process on the torus. Regarding other point processes, we find the optimal rate for the spherical ensemble and the zeros of Gaussian analytic functions.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Spectral Theory in Mathematical Physics
Geometry and complex manifolds
Publication details
- Journal / source
- Mathematika
- Volume
- 72
- Issue
- 2
- Publication date
- 1 April 2026
- Language
- EN