We prove Moderate Deviation estimates for nodal lengths of random spherical harmonics both on the whole sphere and on shrinking spherical domains. Central Limit Theorems for the latter were recently established in Marinucci et al. (2020) and Todino (2020), respectively. Our proofs are based on the combination of a Moderate Deviation Principle by Schulte and Thäle (2016) for sequences of random variables living in a fixed Wiener chaos with a well-known result based on the concept of exponential equivalence
Macci, C., Rossi, M., Todino, A. (2021). Moderate Deviation estimates for Nodal Lengths of Random Spherical Harmonics. ALEA, 18(1 (1 January 2021)), 249-263 [10.30757/ALEA.v18-11].
Moderate Deviation estimates for Nodal Lengths of Random Spherical Harmonics
Rossi, Maurizia
;Todino, Anna Paola
2021
Abstract
We prove Moderate Deviation estimates for nodal lengths of random spherical harmonics both on the whole sphere and on shrinking spherical domains. Central Limit Theorems for the latter were recently established in Marinucci et al. (2020) and Todino (2020), respectively. Our proofs are based on the combination of a Moderate Deviation Principle by Schulte and Thäle (2016) for sequences of random variables living in a fixed Wiener chaos with a well-known result based on the concept of exponential equivalence
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