度量测度空间的锥的收敛性及其在柯西分布中的应用
Convergence of cones of metric measure spaces and its application to Cauchy distribution
AI总结：
本文证明了度量测度空间锥的收敛性可由底空间在Gromov箱、浓度和弱拓扑下的收敛推出，并以此证明适当标度的广义柯西分布在浓度拓扑下随维数趋于无穷收敛到半直线，提供了一个区别于高斯分布和常Ricci曲率流形的新例子。
摘要：
我们证明了，若底空间序列在Gromov箱、浓度和弱拓扑下收敛，则度量测度空间的锥序列也收敛。作为应用，我们证明具有适当标度的广义柯西分布在浓度拓扑下，当维数趋于无穷时收敛到一条半直线。这是一个区别于先前已知例子（如高斯分布和具有常Ricci曲率的典型闭黎曼流形）的新例子。
英文摘要：
We prove that the sequence of cones of metric measure spaces converges if the sequence of base spaces converges in Gromov's box, concentration, and weak topologies. As an application, we show that the generalized Cauchy distribution with suitable scaling converges to a half line in the concentration topology as the dimension diverges to infinity. This is a new example distinguished from previously known examples such as Gaussian distributions and typical closed Riemannian manifolds with constant Ricci curvature.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
