Equidistribution of the conormal cycle of ...
Document type :
Compte-rendu et recension critique d'ouvrage
DOI :
Title :
Equidistribution of the conormal cycle of random nodal sets
Author(s) :
Dang, Nguyen Viet [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Riviere, Gabriel [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Riviere, Gabriel [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Journal title :
Journal of the European Mathematical Society
Publisher :
European Mathematical Society
Publication date :
2018-09-18
ISSN :
1435-9855
English keyword(s) :
eigenfunctions of the Laplacian
Gaussian measures
nodal sets
conormal cycle
Gaussian measures
nodal sets
conormal cycle
HAL domain(s) :
Mathématiques [math]/Théorie spectrale [math.SP]
Mathématiques [math]/Géométrie différentielle [math.DG]
Mathématiques [math]/Probabilités [math.PR]
Mathématiques [math]/Physique mathématique [math-ph]
Mathématiques [math]/Géométrie différentielle [math.DG]
Mathématiques [math]/Probabilités [math.PR]
Mathématiques [math]/Physique mathématique [math-ph]
English abstract : [en]
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 ...
Show more >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 fibers 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.Show less >
Show more >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 fibers 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.Show less >
Language :
Anglais
Popular science :
Non
Comment :
Revised version following referees' comments. Final version J. Eur. Math. Soc. Vol. 20 (12), 2018, 3017-3071.
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