High-frequency asymptotics for subordinated isotropic fields on an Abelian compact group

Group Representations and High-Resolution Central Limit Theorems for Subordinated Spherical Random Fields

We study the weak convergence (in the high-frequency limit) of the frequency components associated with Gaussian-subordinated, spherical and isotropic random fields. In particular, we provide conditions for asymptotic Gaussianity and we establish a new connection with random walks on the the dual of SO(3), which mirrors analogous results previously established for fields defined on Abelian groups (see Marinucci and Peccati (2007)). Our work is motivated by applications to cosmological data analysis, and specifically by the probabilistic modelling and the statistical analysis of the Cosmic Micr…

On Nonlinear Functionals of Random Spherical Eigenfunctions

We prove Central Limit Theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combine asymptotic analysis of higher order moments for Legendre polynomials and, in addition, recent results on Malliavin calculus and Total Variation bounds for Gaussian subordinated fields. We discuss application to geometric functionals like the Defect and invariant statistics, e.g. polyspectra of isotropic spherical random fields. Both of these have relevance for applications, especially in an astrophysical environment.

流形上及更一般时空随机场的非中心极限结果

Noncentral limit results for spatiotemporal random fields on manifolds and beyond

本文针对Hermite秩为2的LRD高斯次时空随机场，在流形和紧凸集上推导了第二Wiener混沌中的非中心极限定理。