arXiv subjects

Pablo García-Arias

Publications and source records attributed to Pablo García-Arias.

2 recordsLinked to original sources

arXiv2026

Quantitative equidistribution of eigenvalues of Random Normal Matrices in the Wasserstein distance

The object of study in this paper is the expected $2$-Wasserstein distance between the empirical measures of several point processes and their respective limit. For this, the main tool developed is a smoothing procedure in Euclidean spaces using the heat equation with Neumann boundary conditions. It is applied to the spectrum of Random Normal Matrices with \textit{reasonable} assumptions on the potential, as well as to Hyperuniform Point Processes such as the infinite Ginibre ensemble and the zero set of the planar Gaussian Analytic Function. In both of these cases, the technique obtains the optimal rate of convergence.

math.PR↗

arXiv2026

Equidistribution of points in the Harmonic ensemble for the Wasserstein distance

We study the asymptotics of the expected Wasserstein distance between the empirical measure of a Point Process and the background volume form. The main DPP studied is the harmonic ensemble, where we get the optimal rate of convergence for homogeneous manifolds of dimension $d\geq 3$, 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.

math.PR↗