论文标题
自由中央限制定理的收敛速率
Rates of convergence in the free central limit theorem
论文作者
论文摘要
我们研究了自由中央限制定理的不一定分布的自由随机变量，其中限制分布是半圆形分布。从适当归一化的自由随机变量和半圆形分布的量度之间的Kolmogorov距离的估计开始，我们显示了自由Lindeberg中央限制定理，并在第三矩的存在下提高了已知的收敛速率。
We study the free central limit theorem for not necessarily identically distributed free random variables where the limiting distribution is the semicircle distribution. Starting from an estimate for the Kolmogorov distance between the measure of suitably normalized sums of free random variables and the semicircle distribution without any moment condition, we show the free Lindeberg central limit theorem and improve the known results on rates of convergence under the conditions of the existence of the third moments.
