稀有事件的非交换定律
Non-commutative law of rare events
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中文总结 AI 辅助
该研究在自由、布尔等非交换概率框架下，建立稀有事件定律和二项式近似的定量版本，给出非交换瓦瑟斯坦距离中的显式误差界，填补了非交换极限定理收敛速率相关文献的空白。
中文摘要 AI 辅助
我们在非交换概率环境（包括自由、布尔和单调卷积框架）中建立了稀有事件定律和二项式近似的定量版本。我们的主要结果为稀有计数的卷积通过非交换泊松分布和二项式分布的近似，给出了非交换瓦瑟斯坦距离中的显式误差界。这些界将张量环境中的经典结果扩展到非交换领域。我们的方法依赖于离散的Lindeberg型插值方案，结合适配每种独立性概念的累积量代数性质。本文呈现的结果填补了非交换极限定理中收敛速度显式速率相关文献的空白。
英文摘要
We establish quantitative versions of the law of rare events and binomial approximations in non-commutative probability settings, including the free, Boolean, and monotone convolution frameworks. Our main results provide explicit error bounds in the non-commutative Wasserstein distance for approximations of convolutions of rare countings by non-commutative Poisson and binomial distributions. These bounds extend classical results from the tensor setting to the non-commutative regime. Our approach relies on a discrete Lindeberg-type interpolation scheme combined with algebraic properties of cumulants adapted to each independence notion. The results presented here fill a gap in the literature concerning explicit rates of convergence in non-commutative limit theorems.
