Nodal deficiency of random spherical harmonics in presence of boundary
Nodal deficiency of random spherical harmonics in presence of boundary
We consider a random Gaussian model of Laplace eigenfunctions on the hemisphere satisfying the Dirichlet boundary conditions along the equator. For this model we find a precise asymptotic law for the corresponding zero density functions, in both short range (around the boundary) and long range (far away from the boundary) …