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- W2963438861 abstract "Given an elliptic self-adjoint pseudo-differential operator $P$ bounded from below, acting on the sections of a Riemannian line bundle over a smooth closed manifold $M$ equipped with some Lebesgue measure, we estimate from above, as $L$ grows to infinity, the Betti numbers of the vanishing locus of a random section taken in the direct sum of the eigenspaces of $P$ with eigenvalues below $L$. These upper estimates follow from some equidistribution of the critical points of the restriction of a fixed Morse function to this vanishing locus. We then consider the examples of the Laplace-Beltrami and the Dirichlet-to-Neumann operators associated to some Riemannian metric on $M$." @default.
- W2963438861 created "2019-07-30" @default.
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- W2963438861 date "2017-01-01" @default.
- W2963438861 modified "2023-10-15" @default.
- W2963438861 title "Betti numbers of random nodal sets of elliptic pseudo-differential operators" @default.
- W2963438861 doi "https://doi.org/10.4310/ajm.2017.v21.n5.a2" @default.
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