High-dimensional metric-measure limit of Stiefel and flag manifolds

Takashi Shioya; Asuka Takatsu

doi:10.1007/s00209-018-2044-y

High-dimensional metric-measure limit of Stiefel and flag manifolds

Takashi Shioya, Asuka Takatsu

SCI - Mathematics

Tokyo Metropolitan University

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We study the high-dimensional limit of (projective) Stiefel and flag manifolds as metric measure spaces in Gromov’s topology. The limits are either the infinite-dimensional Gaussian space or its quotient by some mm-isomorphic group actions, which are drastically different from the manifolds. As a corollary, we obtain some asymptotic estimates of the observable diameter of (projective) Stiefel and flag manifolds.

Original language	English
Pages (from-to)	873-907
Number of pages	35
Journal	Mathematische Zeitschrift
Volume	290
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-018-2044-y
Publication status	Published - 2018 Dec 1

Keywords

Concentration of measure
Gaussian space
Metric measure space
Observable diameter
Pyramid

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title = "High-dimensional metric-measure limit of Stiefel and flag manifolds",

abstract = "We study the high-dimensional limit of (projective) Stiefel and flag manifolds as metric measure spaces in Gromov{\textquoteright}s topology. The limits are either the infinite-dimensional Gaussian space or its quotient by some mm-isomorphic group actions, which are drastically different from the manifolds. As a corollary, we obtain some asymptotic estimates of the observable diameter of (projective) Stiefel and flag manifolds.",

keywords = "Concentration of measure, Gaussian space, Metric measure space, Observable diameter, Pyramid",

author = "Takashi Shioya and Asuka Takatsu",

note = "Funding Information: This work was supported by JSPS KAKENHI Grant Numbers 26400060, 15K17536, 15H05739. Publisher Copyright: {\textcopyright} 2018, Springer-Verlag GmbH Germany, part of Springer Nature.",

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AB - We study the high-dimensional limit of (projective) Stiefel and flag manifolds as metric measure spaces in Gromov’s topology. The limits are either the infinite-dimensional Gaussian space or its quotient by some mm-isomorphic group actions, which are drastically different from the manifolds. As a corollary, we obtain some asymptotic estimates of the observable diameter of (projective) Stiefel and flag manifolds.

KW - Concentration of measure

KW - Gaussian space

KW - Metric measure space

KW - Observable diameter

KW - Pyramid

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ER -

High-dimensional metric-measure limit of Stiefel and flag manifolds

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Keywords

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