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Betti numbers of random nodal sets of elliptic pseudo-differential operators
2017
Asian Journal of Mathematics
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
doi:10.4310/ajm.2017.v21.n5.a2
fatcat:kx673tptlzgtnmolqb6uar645u