论文标题
平面泊松随机组上铁磁能的均质化
Homogenization of ferromagnetic energies on Poisson random sets in the plane
论文作者
论文摘要
我们证明，通过缩放在平面中的泊松随机组上定义的最接近的邻居铁磁能，我们获得的各向同性外围能具有以渐近公式为特征的表面张力。结果依赖于证明相应Voronoi Tessellation的“非常长”或“非常短”边缘的细胞可以被忽略。通过这种方式，我们可以使用几何测量理论工具来定义紧凑的收敛，并使用限制为亚粘附过程的限制定理对Voronoi细胞簇的度量特性进行表征。
We prove that by scaling nearest-neighbour ferromagnetic energies defined on Poisson random sets in the plane we obtain an isotropic perimeter energy with a surface tension characterised by an asymptotic formula. The result relies on proving that cells with `very long' or `very short' edges of the corresponding Voronoi tessellation can be neglected. In this way we may apply Geometry Measure Theory tools to define a compact convergence, and a characterisation of metric properties of clusters of Voronoi cells using limit theorems for subadditive processes.
