HIGH-FREQUENCY ASYMPTOTICS FOR LIPSCHITZ-KILLING CURVATURES OF EXCURSION SETS ON THE SPHERE

• 成果类型: Article
• 署名作者: Marinucci, Domenico; Vadlamani, Sreekar
• 署名单位: University of Rome Tor Vergata; Tata Institute of Fundamental Research (TIFR); TIFR Centre for Applicable Mathematics (CAM), Bengaluru
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1097
• 发表日期: 2016
• 页码: 462-506
• 关键词: FIELDS; formulas; needlets; geometry; maxima

摘要

In this paper, we shall be concerned with geometric functionals and excursion probabilities for some nonlinear transforms evaluated on Fourier components of spherical random fields. In particular, we consider both random spherical harmonics and their smoothed averages, which can be viewed as random wavelet coefficients in the continuous case. For such fields, we consider smoothed polynomial transforms; we focus on the geometry of their excursion sets, and we study their asymptotic behaviour, in the high frequency sense. We focus on the analysis of Euler-Poincare characteristics, which can be exploited to derive extremely accurate estimates for excursion probabilities. The present analysis is motivated by the investigation of asymmetries and anisotropies in cosmological data. The statistics we focus on are also suitable to deal with spherical random fields which can only be partially observed, the canonical example being provided by the masking effect of the Milky Way on Cosmic Microwave Background (CMB) radiation data.