Claudio Durastanti, researcher at the Department of Basic and Applied Sciences for Engineering (SBAI) of Sapienza University, was our guest at the D2 Seminar Series presenting his talk on “Spherical Poisson Waves“.
During his talk, he discussed a model of Poisson random waves defined in the sphere, to study Quantitative Central Limit Theorems when both the rate of the Poisson process (that is, the expected number of the observations sampled at a fixed time) 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.
What are we talking about when we talk about Spherical Poisson Waves?
A spherical Poisson random wave (or random eigenfunction) is the superposition of a random number of deterministic waves, centered at points uniformly distributed on the sphere.