Spherical Poisson Waves

Solesne Bourguin; Claudio Durastanti; Domenico Marinucci; Anna Paola Todino

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arXiv · 2203.04721

Spherical Poisson Waves

Solesne Bourguin·Claudio Durastanti·Domenico Marinucci·Anna Paola Todino

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Abstract

We introduce a model of Poisson random waves in $\mathbb{S}^{2}$ 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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Solesne Bourguin, Claudio Durastanti, Domenico Marinucci, Anna Paola Todino. 2022-03-09. Spherical Poisson Waves. https://arxiv.org/abs/2203.04721

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