Spectral convergence of high-dimensional spheres to Gaussian spaces

2021/06/17 by Asuka Takatsu, Takatsu, Asuka · 1 citation
Mathematics · #35P20 #58J50 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Numerical methods in inverse problems #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2106.09452

openalex publication_date 2021/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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→ ∞. 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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