High-dimensional ellipsoids converge to Gaussian spaces
High-dimensional ellipsoids converge to Gaussian spaces
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DOI：
10.2969/jmsj/86648664
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发表时间：
2020-03
影响因子：
0.7
通讯作者：
Daisuke Kazukawa;T. Shioya
中科院分区：
文献类型：
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作者：
Daisuke Kazukawa;T. Shioya
我们证明了收敛的（固体）椭球高斯空间在格罗莫夫的浓度/弱拓扑的维数发散到无穷大。这给出了第一个发现的例子，一个不可约的非平凡收敛序列的浓度拓扑，其中'不可约的非平凡'大致意味着不从利维家庭也不箱收敛序列。
We prove the convergence of (solid) ellipsoids to a Gaussian space in Gromov's concentration/weak topology as the dimension diverges to infinity. This gives the first discovered example of an irreducible nontrivial convergent sequence in the concentration topology, where 'irreducible nontrivial' roughly means to be not constructed from Levy families nor box convergent sequences.