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math.PR2021
On the behavior of nodal lines near the boundary for Laplace eigenfunctions on the square
Oleksiy Klurman, Andrea Sartori
We are interested in the effect of Dirichlet boundary conditions on the nodal length of Laplace eigenfunctions. We study random Gaussian Laplace eigenfunctions on the two dimension…
math.PR2021
Expected nodal volume for non-Gaussian random band-limited functions
Zakhar Kabluchko, Andrea Sartori, Igor Wigman
The asymptotic law for the expected nodal volume of random non-Gaussian monochromatic band-limited functions is determined in vast generality. Our methods combine microlocal analyt…