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arXiv · 1507.01063

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

Takashi Shioya·Asuka Takatsu
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Abstract

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

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Takashi Shioya, Asuka Takatsu. 2015-07-04. High-dimensional metric-measure limit of Stiefel and Grassmann manifolds. https://arxiv.org/abs/1507.01063

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