April, 2024 High-dimensional ellipsoids converge to Gaussian spaces
Daisuke KAZUKAWA, Takashi SHIOYA
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J. Math. Soc. Japan 76(2): 473-501 (April, 2024). DOI: 10.2969/jmsj/86648664

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 Lévy families nor box convergent sequences.

Funding Statement

This work was supported by JSPS KAKENHI Grant Number 19K03459 and 17J02121.

Citation

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Daisuke KAZUKAWA. Takashi SHIOYA. "High-dimensional ellipsoids converge to Gaussian spaces." J. Math. Soc. Japan 76 (2) 473 - 501, April, 2024. https://doi.org/10.2969/jmsj/86648664

Information

Received: 11 March 2021; Revised: 17 October 2022; Published: April, 2024
First available in Project Euclid: 17 October 2023

Digital Object Identifier: 10.2969/jmsj/86648664

Subjects:
Primary: 53C23

Keywords: box distance , concentration topology , ellipsoid , Gaussian space , observable distance , pyramid

Rights: Copyright ©2024 Mathematical Society of Japan

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Vol.76 • No. 2 • April, 2024
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