论文标题
在KAC球体上重新制定措施的混乱
Chaos for rescaled measures on Kac's sphere
论文作者
论文摘要
在本文中，我们研究了一种相对新颖的方法，它构建了KAC球体支持的混乱序列，该序列是作为$ n $ i.i.d.的向量定律获得的。变量重新缩放后具有单位平均能量。我们表明，随着$ n $的增加，就wasserstein距离而言，此序列是混乱的，从恩格斯坦距离，$ l^1 $，从熵意义上讲以及在渔民的信息意义上。对于许多结果，我们以$ n $提供明确的多项式订单率。在此过程中，我们通过放松订单$ 6 $ $ 6 $ $ 4+ε$的有限矩要求来改善Haurey和Mischler的定量熵混乱。
In this article we study a relatively novel way of constructing chaotic sequences of probability measures supported on Kac's sphere, which are obtained as the law of a vector of $N$ i.i.d. variables after it is rescaled to have unit average energy. We show that, as $N$ increases, this sequence is chaotic in the sense of Kac, with respect to the Wasserstein distance, in $L^1$, in the entropic sense, and in the Fisher information sense. For many of these results, we provide explicit rates of polynomial order in $N$. In the process, we improve a quantitative entropic chaos result of Haurey and Mischler by relaxing the finite moment requirement on the densities from order $6$ to $4+ε$.
