论文标题
光谱准相关性和算术随机波的淋巴结长度的相变
Spectral quasi correlations and phase-transitions for the nodal length of Arithmetic Random Waves
论文作者
论文摘要
光谱准相关性是位于同一圆上的晶格点的一小部分。我们表明，对于代表两个正方形总和的通用整数，没有光谱准相关。此外，我们将结果应用于小尺度上的算术随机波的淋巴结长度：我们表明存在一种相位传输，用于在Planck尺度上方以对数功率以对数功率的分布分布。此外，我们为算术和贝瑞随机波之间存在中间相的存在提供了有力的证据。
Spectral quasi correlations are small sums of lattice points lying on the same circle; we show that, for generic integers representable as the sum of two squares, there are no spectral quasi-correlations. Moreover, we apply our result to study the nodal length of Arithmetic Random Waves at small scales: we show that there exists a phase-transition for the distribution of the nodal length at a logarithmic power above Planck-scale. Furthermore, we give strong evidence for the existence of an intermediate phase between Arithmetic and Berry's random waves.
