In this paper, we show that the Lipschitz-Killing curvatures for the excursion sets of arithmetic random waves (toral Gaussian eigenfunctions) are dominated, in the high-frequency regime, by a single chaotic component. The latter can be written as a simple explicit function of the threshold parameter times the centered norm of these random fields; as a consequence, these geometric functionals are fully correlated in the high-energy limit. The derived formulae show a clear analogy with related results on the round unit sphere and suggest the existence of a general formula for geometric functionals of random eigenfunctions on Riemannian manifolds.

Cammarota, V., Marinucci, D., Rossi, M. (2023). Lipschitz-Killing Curvatures for Arithmetic Random Waves. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE, 24(2), 1095-1147 [10.2422/2036-2145.202010_065].

Lipschitz-Killing Curvatures for Arithmetic Random Waves

Rossi, Maurizia
2023

Abstract

In this paper, we show that the Lipschitz-Killing curvatures for the excursion sets of arithmetic random waves (toral Gaussian eigenfunctions) are dominated, in the high-frequency regime, by a single chaotic component. The latter can be written as a simple explicit function of the threshold parameter times the centered norm of these random fields; as a consequence, these geometric functionals are fully correlated in the high-energy limit. The derived formulae show a clear analogy with related results on the round unit sphere and suggest the existence of a general formula for geometric functionals of random eigenfunctions on Riemannian manifolds.
Articolo in rivista - Articolo scientifico
Random waves; Wiener chaos; Minkowski functionals; Limit theorems
English
26-giu-2023
2023
24
2
1095
1147
none
Cammarota, V., Marinucci, D., Rossi, M. (2023). Lipschitz-Killing Curvatures for Arithmetic Random Waves. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE, 24(2), 1095-1147 [10.2422/2036-2145.202010_065].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/354989
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