高维椭球体收敛于高斯空间

Pub Date : 2023-10-17 DOI:10.2969/jmsj/86648664
Daisuke Kazukawa, Takashi Shioya
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引用次数: 5

摘要

我们证明了在Gromov集中/弱拓扑中(实体)椭球体在维数发散到无穷远时收敛于高斯空间。这给出了在集中拓扑中发现的第一个不可约非平凡收敛序列的例子,其中“不可约非平凡”大致意味着不是由lsamvy族或盒收敛序列构造的。
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High-dimensional ellipsoids converge to Gaussian spaces
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 Lévy families nor box convergent sequences.
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