论文标题
$ \ mathbb {s}^2 \ times \ mathbb {r} $在$ \ mathbb {s}^$上的各向同性固定字段的经验度量的非宇宙波动
Non-Universal Fluctuations of the Empirical Measure for Isotropic Stationary Fields on $\mathbb{S}^2 \times \mathbb{R}$
论文作者
论文摘要
在本文中，我们考虑在$ \ mathbb {s}^2 \ times \ times \ mathbb {r} $上定义的各向同性和固定的真实高斯随机字段，我们研究了$ t \ rightarrow +\ rightarrow +\ infty $ in $ \ mathbbbbbbbbbbbbbb \ s} @ s^2 2^2^2^2^2^2^2^2^2阈值，涵盖了这两种情况，当该场表现出短而长的记忆，即可整合且不可集成的时间协方差。事实证明，限制分布不是通用的，取决于内存参数和阈值。特别是，在长期记忆案例中，浆果取消现象的一种形式发生在零级别，诱导了方差率和限制定律的相变。
In this paper, we consider isotropic and stationary real Gaussian random fields defined on $\mathbb{S}^2\times\mathbb{R}$ and we investigate the asymptotic behavior, as $T\rightarrow +\infty$, of the empirical measure (excursion area) in $\mathbb{S}^2\times\mathbb{R}$ at any threshold, covering both cases when the field exhibits short and long memory, i.e. integrable and non-integrable temporal covariance. It turns out that the limiting distribution is not universal, depending both on the memory parameters and the threshold. In particular, in the long memory case a form of Berry's cancellation phenomenon occurs at zero-level, inducing phase transitions for both variance rates and limiting laws.
