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- W4301737515 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.
- W4301737515 created "2022-10-05" @default.
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- W4301737515 date "2014-06-03" @default.
- W4301737515 modified "2023-09-28" @default.
- W4301737515 title "Betti numbers of random nodal sets of elliptic pseudo-differential operators" @default.
- W4301737515 doi "https://doi.org/10.48550/arxiv.1406.0934" @default.
- W4301737515 hasPublicationYear "2014" @default.
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