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. 
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