Mathematical analysis
Non-universality of the Nazarov–Sodin constant
[Non-universalité de la constante de Nazarov–Sodin]

Présenté par : the Editorial Board

Kurlberg, Pär1 ; Wigman, Igor2
1 Department of Mathematics, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden
2 Department of Mathematics, King's College London, UK
Comptes Rendus. Mathématique, Tome 353 (2015) no. 2, pp. 101-104.

On démontre que la constante de Nazarov–Sodin, qui, à un changement d'échelle près, donne le terme principal de l'ordre de croissance du nombre de composantes nodales d'un champ aléatoire gaussien, dépend effectivement du champ. On en déduit que le résultat reste vrai pour les « ondes aléatoires arithmétiques », c'est-à-dire pour les fonctions propres du laplacien aléatoire sur un tore.

We prove that the Nazarov–Sodin constant, which up to a natural scaling gives the leading order growth for the expected number of nodal components of a random Gaussian field, genuinely depends on the field. We then infer the same for “arithmetic random waves”, i.e. random toral Laplace eigenfunctions.

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Accepté le :
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DOI : 10.1016/j.crma.2014.09.026
Kurlberg, Pär 1 ; Wigman, Igor 2

1 Department of Mathematics, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden
2 Department of Mathematics, King's College London, UK 
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Kurlberg, Pär; Wigman, Igor. Non-universality of the Nazarov–Sodin constant. Comptes Rendus. Mathématique, Tome 353 (2015) no. 2, pp. 101-104. doi : 10.1016/j.crma.2014.09.026. http://www.numdam.org/articles/10.1016/j.crma.2014.09.026/

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