论文标题
关于混合 - 标志和相关衰减速率
On mix-norms and the rate of decay of correlations
论文作者
论文摘要
混合的两个定量概念是相关性的衰减和混合 - 衰减的衰减（负Sobolev Norm），并且可以通过这些量的衰减速率来测量混合的强度。从二元性中，相关性被混合 - 统一统一。但是它们可以比混合 - 标准更快地腐烂吗？我们通过构建与可观察到的相关性的可观察到的相关性来回答这个问题，该相关是任意接近达到混合仪的衰减率的。因此，混合仪是在均匀的意义和渐近意义上的相关性衰减速率最清晰的速度。此外，存在一个可观察到的相关性，而当且仅当混合 - 衰减的速率通过其投影到低频傅立叶傅立叶模式下实现时，它的相关性就与混合 - 标准相同。在这种情况下，混合的函数称为Q-循环。否则是Q传播。我们使用此分类来研究几个示例，并提出问题以供未来的调查。
Two quantitative notions of mixing are the decay of correlations and the decay of a mix-norm -- a negative Sobolev norm -- and the intensity of mixing can be measured by the rates of decay of these quantities. From duality, correlations are uniformly dominated by a mix-norm; but can they decay asymptotically faster than the mix-norm? We answer this question by constructing an observable with correlation that comes arbitrarily close to achieving the decay rate of the mix-norm. Therefore the mix-norm is the sharpest rate of decay of correlations in both the uniform sense and the asymptotic sense. Moreover, there exists an observable with correlation that decays at the same rate as the mix-norm if and only if the rate of decay of the mix-norm is achieved by its projection onto low-frequency Fourier modes. In this case, the function being mixed is called q-recurrent; otherwise it is q-transient. We use this classification to study several examples and raise questions for future investigations.
