We prove equidistribution at shrinking scales for the monochromatic ensemble on a compact Riemannian manifold of any dimension. This ensemble on an arbitrary manifold takes a slowly growing spectral window in order to synthesize a random function. With high probability, equidistribution takes place close to the optimal wave scale and simultaneously over the whole manifold. The proof uses Weyl's law to approximate the two-point correlation function of the ensemble, and a Chernoff bound to deduce concentration.

中文翻译：

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紧凑流形上单色随机波的缩标等分布

我们证明了在任何维度的紧凑黎曼流形上的单色系综在收缩尺度上的等分布。这个在任意流形上的集合需要一个缓慢增长的光谱窗口来合成一个随机函数。以高概率，等分布发生在接近最佳波浪尺度并同时在整个流形上发生。该证明使用外尔定律来逼近系综的两点相关函数，并使用切尔诺夫必然推导出浓度。