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arXiv · 2308.10497

Asymptotics of Kantorovich Distance for Empirical Measures of the Laguerre Model

Huaiqian Li·Bingyao Wu
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Abstract

We estimate the rate of convergence for the Kantorovich (or Wasserstein) distance between empirical measures of i.i.d. random variables associated with the Laguerre model of order $\alpha$ on $(0,\infty)^N$ and their common law, which is not compactly supported and has no rotational symmetry. Compared with the Gaussian case, our result is sharp provided the parameter $\alpha$ and the dimension $N$ are chosen in a specified regime.

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Huaiqian Li, Bingyao Wu. 2023-08-21. Asymptotics of Kantorovich Distance for Empirical Measures of the Laguerre Model. https://arxiv.org/abs/2308.10497

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