5 papers · 1 filter
Statistics on Yau's conjecture: Variance asymptotics
Michele Stecconi, Anna Paola Todino
We investigate the probabilistic counterpart of Yau's conjecture on the nodal volume of Laplace eigenfunctions on compact manifolds, by studying the high-frequency variance asympto…
Berry-Heisenberg Random Waves
Marco Carfagnini, Anna Paola Todino
We construct a new family of random fields on the Heisenberg group , the sub-Riemannian analog of . These fields are generalized random eigenfunctions o…
New chaos decomposition of Gaussian nodal volumes
Michele Stecconi, Anna Paola Todino
We investigate the random variable defined by the volume of the zero set of a smooth Gaussian field, on a general Riemannian manifold possibly with boundary, a fundamental object i…
On the Euler-Poincaré Characteristic of the planar Berry's random wave: fluctuations and a perturbation study
Elena Di Bernardino, Radomyra Shevchenko, Anna Paola Todino
We prove the Central Limit Theorem for the Euler-Poincaré characteristic of Berry's random wave model in a growing domain. We also show Gaussian fluctuations for a class of Berry'…
Small fluctuations for time-dependent spherical random fields
Marco Carfagnini, Anna Paola Todino
We consider time-dependent space isotropic and time stationary spherical Gaussian random fields. We establish Chung's law of the iterated logarithm and solve the small probabilitie…