Spherical Poisson Waves

2022/03/09 by Solesne Bourguin, Claudio Durastanti, Bourguin, Solesne +5 · 4 citations
Computer Science · #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2203.04721

Abstract

We introduce a model of Poisson random waves in \mathbbS² and we study Quantitative Central Limit Theorems when both the rate of the Poisson process and the energy (i.e., frequency) of the waves (eigenfunctions) diverge to infinity. We consider finite-dimensional distributions, harmonic coefficients and convergence in law in functional spaces, and we investigate carefully the interplay between the rates of divergence of eigenvalues and Poisson governing measures.

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• The Fourth-Moment Theorem on Hilbert Spaces
• A Caveat on Metrizing Convergence in Distribution on Hilbert Spaces
• Spherical Poisson Needlets with Shrinking Bandwidth
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