论文标题
部分可观测时空混沌系统的无模型预测
A theory of singular values for finite free probability
论文作者
论文摘要
我们引入了矩形矩阵的有限版本的自由概率，这相当于多项式奇异值的操作。我们表明我们可以从自由概率复制转换，并且渐近地存在从矩形有限的自由概率到矩形自由概率的收敛性。最后，我们表明，在这个新框架中可以明确地将经典的分布结果（例如大数字定律或中心限制定理）显式，在此新框架中，随机变量被多项式替换。
We introduce a finite version of free probability for rectangular matrices that amounts to operations on singular values of polynomials. We show that we can replicate the transforms from free probability, and that asymptotically there is convergence from rectangular finite free probability to rectangular free probability. Lastly, we show that classical distribution results such as a law of large numbers or a central limit theorem can be made explicit in this new framework where random variables are replaced by polynomials.
