Corpus ID: 235458032

# Spectral convergence of high-dimensional spheres to Gaussian spaces

@inproceedings{Takatsu2021SpectralCO,
title={Spectral convergence of high-dimensional spheres to Gaussian spaces},
author={Asuka Takatsu},
year={2021}
}
We prove that the spectral structure on the N -dimensional standard sphere of radius (N − 1) 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 → ∞. 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.
2 Citations
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