Moderate Deviation estimates for Nodal Lengths of Random Spherical Harmonics

Claudio Macci, Maurizia Rossi, Anna Paola Todino

Published 2020-06-09Version 1

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, Rossi and Wigman (2020) and Todino (2020+) respectively. Our proofs are based on the combination of a Moderate Deviation Principle by Schulte and Th\"ale (2016) for sequences of random variables living in a fixed Wiener chaos with a well-known result based on the concept of exponential equivalence.