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arXiv · 1406.1396

A rate of convergence for the circular law for the complex Ginibre ensemble

Elizabeth S. Meckes·Mark W. Meckes
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Abstract

We prove rates of convergence for the circular law for the complex Ginibre ensemble. Specifically, we bound the expected $L_p$-Wasserstein distance between the empirical spectral measure of the normalized complex Ginibre ensemble and the uniform measure on the unit disc, both in expectation and almost surely. For $1 \le p \le 2$, the bounds are of the order $n^{-1/4}$, up to logarithmic factors.

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Elizabeth S. Meckes, Mark W. Meckes. 2014-06-05. A rate of convergence for the circular law for the complex Ginibre ensemble. https://arxiv.org/abs/1406.1396

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