High-dimensional ellipsoids converge to Gaussian spaces
Metric Geometry
2020-03-12 v1 Differential Geometry
Abstract
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.
Cite
@article{arxiv.2003.05105,
title = {High-dimensional ellipsoids converge to Gaussian spaces},
author = {Daisuke Kazukawa and Takashi Shioya},
journal= {arXiv preprint arXiv:2003.05105},
year = {2020}
}
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28 pages