论文标题
定量弱混合以进行随机取代
Quantitative weak mixing for random substitution tilings
论文作者
论文摘要
对于$ n $兼容的替代规则，$ m $ prototiles $ t_1，\ dots，t_m $，考虑通过随机应用不同的替代规则构建的瓷砖和平铺空间。这些给出了（全球）随机替代的瓷砖。在本文中，我获得了$ \ Mathbb {r}^d $动作在瓷砖空间上的扭曲的厄贡积分的增长界限，该范围在光谱措施的较低局部维度上给出了下限。对于具有一些额外规律性的功能，可以获得较低局部维度的均匀边界。这里的结果将Bufetov-Solomyak的结果扩展到较高维度的瓷砖。
For $N$ compatible substitution rules on $M$ prototiles $t_1,\dots,t_M$, consider tilings and tiling spaces constructed by applying the different substitution rules at random. These give (globally) random substitution tilings. In this paper I obtain bounds for the growth on twisted ergodic integrals for the $\mathbb{R}^d$ action on the tiling space which give lower bounds on the lower local dimension of spectral measures. For functions with some extra regularity, uniform bounds on the lower local dimension are obtained. The results here extends results of Bufetov-Solomyak to tilings of higher dimensions.
