齐次和各向同性张量值随机场的谱展开
Spectral Expansions of Homogeneous and Isotropic Tensor-Valued Random Fields
摘要：
我们建立了在$3$维欧几里得空间$E^3$和$E^3$上的对称秩$2$张量空间$\mathsf{S}^2(E^3)$中取值的齐次和各向同性随机场的谱展开式.前者是湍流速度的模型，而后者是随机应力张量或随机电导率张量的模型。我们发现了随机场理论和有限维凸矩阵理论之间的联系。
英文摘要：
We establish spectral expansions of homogeneous and isotropic random fields taking values in the $3$-dimensional Euclidean space $E^3$ and in the space $\mathsf{S}^2(E^3)$ of symmetric rank $2$ tensors over $E^3$. The former is a model of turbulent fluid velocity, while the latter is a model for the random stress tensor or the random conductivity tensor. We found a link between the theory of random fields and the theory of finite-dimensional convex compacta.
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