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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.18313 |
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| _version_ | 1866910059120820224 |
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| author | Arias, P. García |
| author_facet | Arias, P. García |
| contents | 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, as well as to several families of Homogeneous Point Processes such as the infinite Ginibre ensemble, the Bessel ensemble, and the zero set of the planar Gaussian Analytic Function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18313 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantitative equidistribution of eigenvalues of Random Normal Matrices in the Wasserstein distance Arias, P. García Probability 49Q22, 60B20, 60G55 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, as well as to several families of Homogeneous Point Processes such as the infinite Ginibre ensemble, the Bessel ensemble, and the zero set of the planar Gaussian Analytic Function. |
| title | Quantitative equidistribution of eigenvalues of Random Normal Matrices in the Wasserstein distance |
| topic | Probability 49Q22, 60B20, 60G55 |
| url | https://arxiv.org/abs/2603.18313 |