NON-UNIVERSAL FLUCTUATIONS OF THE EMPIRICAL MEASURE FOR ISOTROPIC STATIONARY FIELDS ON S2 x R

• 成果类型: Article
• 署名作者: Marinucci, Domenico; Rossi, Maurizia; Vidotto, Anna
• 署名单位: University of Rome Tor Vergata; University of Milano-Bicocca; G d'Annunzio University of Chieti-Pescara
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1648
• 发表日期: 2021
• 页码: 2311-2349
• 关键词: CENTRAL LIMIT-THEOREMS; nodal length; nonlinear functionals; brownian-motion; CONVERGENCE; SEQUENCES

摘要

In this paper, we consider isotropic and stationary real Gaussian random fields defined on S-2 x R and we investigate the asymptotic behavior, as T -> +infinity, of the empirical measure (excursion area) in S-2 x [0, T] at any threshold, covering both cases when the field exhibits short and long memory, that is, integrable and nonintegrable temporal covariance. It turns out that the limiting distribution is not universal, depending both on the memory parameters and the threshold. In particular, in the long memory case a form of Berry's cancellation phenomenon occurs at zero-level, inducing phase transitions for both variance rates and limiting laws.