King's College London

Research portal

The Asymptotic Equivalence of the Sample Trispectrum and the Nodal Length for Random Spherical Harmonics

Research output: Contribution to journalArticlepeer-review

Domenico Marinucci, Maurizia Rossi, Igor Wigman

Original languageEnglish
Pages (from-to)374-390
Number of pages17
JournalAnnales de l’Institut Henri Poincaré, Probabilités et Statistiques
Issue number1
Early online date3 Feb 2020
Accepted/In press30 Jan 2019
E-pub ahead of print3 Feb 2020


King's Authors


We study the asymptotic behaviour of the nodal length of random 2d-spherical harmonics f of high degree ℓ → ∞, i.e. the length of their zero set f -1 (0). It is found that the nodal lengths are asymptotically equivalent, in the L 2-sense, to the "gsample trispectrum", i.e., the integral of H 4(f (x)), the fourth-order Hermite polynomial of the values of f . A particular by-product of this is a Quantitative Central Limit Theorem (in Wasserstein distance) for the nodal length, in the high energy limit.

Download statistics

No data available

View graph of relations

© 2020 King's College London | Strand | London WC2R 2LS | England | United Kingdom | Tel +44 (0)20 7836 5454