Abstract
We introduce a model of Poisson random waves in 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 rate of divergence of eigenvalues and Poisson governing measures.
Funding Statement
The research by SB was supported in part by the Simons Foundation grant 635136. The research by CD was supported by Sapienza Grant RM12117A6212F538. The research by DM was partially supported by the MIUR Departments of Excellence Program MatModTov and by Prin 2022 Grafia.
Citation
Solesne Bourguin. Claudio Durastanti. Domenico Marinucci. Anna Paola Todino. "Spherical Poisson waves." Electron. J. Probab. 29 1 - 27, 2024. https://doi.org/10.1214/23-EJP1071
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