论文标题
真正高斯零的方差线性
Variance linearity for real Gaussian zeros
论文作者
论文摘要
我们在实际线上研究了零固定的高斯过程的零集，尤其是在所有通用性的大间隔上的点数的差异。我们证明，这个点过程绝不是超均匀的，即，方差至少是线性的，并且提供了具有线性方差的必要条件，即接近尖锐的线性方差。我们研究了对称的Bernoulli卷积类别的类别，并举例说明零集是超刚性，弱混合而不是超均匀的。
We investigate the zero set of a stationary Gaussian process on the real line, and in particular give lower bounds for the variance of the number of points on a large interval, in all generality. We prove that this point process is never hyperuniform, i.e. the variance is at least linear, and give necessary conditions to have linear variance, which are close to be sharp. We study the class of symmetric Bernoulli convolutions and give an example where the zero set is super rigid, weakly mixing, and not hyperuniform.
