高维椭球收敛到高斯空间
High-dimensional ellipsoids converge to Gaussian spaces
摘要:
证明了当维数发散到无穷大时,在Gromov的集中/弱拓扑中(实心)椭球收敛到高斯空间。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框收敛序列。
英文摘要:
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.
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