Equidistribution of the conormal cycle of ...
Type de document :
Compte-rendu et recension critique d'ouvrage
DOI :
Titre :
Equidistribution of the conormal cycle of random nodal sets
Auteur(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]
Titre de la revue :
Journal of the European Mathematical Society
Éditeur :
European Mathematical Society
Date de publication :
2018-09-18
ISSN :
1435-9855
Mot(s)-clé(s) en anglais :
eigenfunctions of the Laplacian
Gaussian measures
nodal sets
conormal cycle
Gaussian measures
nodal sets
conormal cycle
Discipline(s) HAL :
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]
Résumé en anglais : [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 ...
Lire la suite >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.Lire moins >
Lire la suite >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.Lire moins >
Langue :
Anglais
Vulgarisation :
Non
Commentaire :
Revised version following referees' comments. Final version J. Eur. Math. Soc. Vol. 20 (12), 2018, 3017-3071.
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