Geodesic
Equidistribution of the conormal cycle of random nodal sets
Journal of the European Mathematical Society, Tome 20 (2018) no. 12, pp. 3017-3071 Cet article a éte moissonné depuis la source EMS Press

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We study the asymptotic properties of the conormal cycle of nodal sets associated to a random superposition of eigenfunctions of the Laplacian on a smooth compact Riemannian manifold without boundary. In the case where the dimension is odd, we show that the expectation of the corresponding current of integration equidistributes on the fibres of the cotangent bundle. In the case where the dimension is even, we obtain an upper bound of lower order on the expectation. Using recent results of Alesker, we also deduce some properties on the asymptotic expectation of any smooth valuation including the Euler characteristic of random nodal sets.
DOI : 10.4171/jems/828
Classification : 58-XX, 35-XX, 60-XX
Keywords: Eigenfunctions of the Laplacian, Gaussian measures, nodal sets, conormal cycle 
@article{JEMS_2018_20_12_a2,
     author = {Nguyen Viet Dang and Gabriel Rivi\`ere},
     title = {Equidistribution of the conormal cycle of random nodal sets},
     journal = {Journal of the European Mathematical Society},
     pages = {3017--3071},
     year = {2018},
     volume = {20},
     number = {12},
     doi = {10.4171/jems/828},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/828/}
}
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Nguyen Viet Dang; Gabriel Rivière. Equidistribution of the conormal cycle of random nodal sets. Journal of the European Mathematical Society, Tome 20 (2018) no. 12, pp. 3017-3071. doi: 10.4171/jems/828

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