论文标题
零计数和固定高斯过程的节点长度的估计过度拥挤的估计值
Overcrowding estimates for zero count and nodal length of stationary Gaussian processes
论文作者
论文摘要
假设在$ \ mathbb {r} $（或$ {\ mathbb {r}}^2 $）上采取某些条件，以$ \ mathbb {r} $（或$ \ mathbb {r} $）进行的某些条件，我们表明，事件的可能性是，它们在间隔中的零计数（在平方域中，nodal nodal nodal nodal in $ n $ n $ n $ n Ignession toce of n $ n ocival of n $ nige contery（$ n $ n）均大于$ n $ nike counter（nign）。该方形域中的节点长度在$ n $中成倍小。
Assuming certain conditions on the spectral measures of centered stationary Gaussian processes on $\mathbb{R}$ (or ${\mathbb{R}}^2$), we show that the probability of the event that their zero count in an interval (resp., nodal length in a square domain) is larger than $n$, where $n$ is much larger than the expected value of the zero count in that interval (resp., nodal length in that square domain), is exponentially small in $n$.
