Moderate Deviation estimates for Nodal Lengths of Random Spherical Harmonics
Probability
2020-10-30 v2
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, 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.
Cite
@article{arxiv.2006.05290,
title = {Moderate Deviation estimates for Nodal Lengths of Random Spherical Harmonics},
author = {Claudio Macci and Maurizia Rossi and Anna Paola Todino},
journal= {arXiv preprint arXiv:2006.05290},
year = {2020}
}
Comments
Revised according to referee's comments. To appear in ALEA