We study the correlation between the nodal length of random spherical harmonics and the length of a nonzero level set. We show that the correlation is asymptotically zero, while the partial correlation after removing the effect of the random L2-norm of the eigenfunctions is asymptotically one.
Marinucci, D., Rossi, M. (2021). On the Correlation Between Nodal and Nonzero Level Sets for Random Spherical Harmonics. ANNALES HENRI POINCARE', 22(1), 275-307 [10.1007/s00023-020-00985-3].
On the Correlation Between Nodal and Nonzero Level Sets for Random Spherical Harmonics
Rossi M.
2021
Abstract
We study the correlation between the nodal length of random spherical harmonics and the length of a nonzero level set. We show that the correlation is asymptotically zero, while the partial correlation after removing the effect of the random L2-norm of the eigenfunctions is asymptotically one.
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