Spectral convergence of high-dimensional spheres to Gaussian spaces

Asuka Takatsu

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arXiv · 2106.09452

Spectral convergence of high-dimensional spheres to Gaussian spaces

Asuka Takatsu

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Abstract

We prove that the spectral structure on the $N$-dimensional standard sphere of radius $(N-1)^{1/2}$ compatible with a projection onto the first $n$-coordinates converges to the spectral structure on the $n$-dimensional Gaussian space with variance $1$ as $N\to \infty$. We also show the analogue for the first Dirichlet eigenvalue and its eigenfunction on a ball in the sphere and on a half-space in the Gaussian space.

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BibTeX RIS

Asuka Takatsu. 2021-06-17. Spectral convergence of high-dimensional spheres to Gaussian spaces. https://arxiv.org/abs/2106.09452

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