We introduce a model of Poisson random waves in S2 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.
Bourguin, S., Durastanti, C., Marinucci, D., Todino, A.p. (2024). Spherical Poisson waves. ELECTRONIC JOURNAL OF PROBABILITY, 29 [10.1214/23-ejp1071].
Spherical Poisson waves
Marinucci, Domenico
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2024-01-01
Abstract
We introduce a model of Poisson random waves in S2 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.File in questo prodotto:
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