论文标题
部分可观测时空混沌系统的无模型预测
Improved concentration of Laguerre and Jacobi ensembles
论文作者
论文摘要
我们考虑渐近极限，其中Laguerre和Jacobi合奏定义中的某些参数有所不同。在这些限制中，Dette，Imhof和Nagel证明了达到线性转化，共同体的关节概率分布分别越来越集中在Laguerre和Jacobi多项式的零周围。在本文中，我们提高了浓度界限。我们的证明与原始参考文献中的证明相似，但是错误分析得到了改进，并且可以说更简单。在雅各比集合的第一矩和第二矩中，我们进一步提高了上述结果所隐含的浓度界限。
We consider the asymptotic limits where certain parameters in the definitions of the Laguerre and Jacobi ensembles diverge. In these limits, Dette, Imhof, and Nagel proved that up to a linear transformation, the joint probability distributions of the ensembles become more and more concentrated around the zeros of the Laguerre and Jacobi polynomials, respectively. In this paper, we improve the concentration bounds. Our proofs are similar to those in the original references, but the error analysis is improved and arguably simpler. For the first and second moments of the Jacobi ensemble, we further improve the concentration bounds implied by our aforementioned results.
