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math.PR2023
Laguerre Expansion for Nodal Volumes and Applications
Domenico Marinucci, Maurizia Rossi, Anna Paola Todino
We investigate the nodal volume of random hyperspherical harmonics on the -dimensional unit sphere (). We exploit an orth…
math.PR2023
Fluctuations of Polyspectra in Spherical and Euclidean Random Wave Models
Francesco Grotto, Leonardo Maini, Anna Paola Todino
We consider polynomial transforms (polyspectra) of Berry's model -- the Euclidean Random Wave model -- and of Random Hyperspherical Harmonics. We determine the asymptotic behavior…
math.PR2023
No smooth Phase Transition for the Nodal Length of Band-limited Spherical Random Fields
Anna Paola Todino
In this paper, we investigate the variance of the nodal length for band-limited spherical random waves. When the frequency window includes a number of eigenfunctions that grows lin…