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math.PR2021★ 1 cited
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.PR2019★ 5 cited
Boundary effect on the nodal length for Arithmetic Random Waves, and spectral semi-correlations
Valentina Cammarota, Oleksiy Klurman, Igor Wigman
We test M. Berry's ansatz on nodal deficiency in presence of boundary. The square billiard is studied, where the high spectral degeneracies allow for the introduction of a Gaussian…