Coordinates changed random fields on the sphere

TL;DR

This paper introduces a method to construct time-dependent random fields on the sphere using coordinate changes and subordination, analyzing their angular power spectrum and connections to PDE solutions with random initial conditions.

Contribution

It presents a novel approach to generating and studying random fields on the sphere via coordinate transformations and subordination techniques.

Findings

Derived properties of the angular power spectrum for the constructed fields.

Established links between these random fields and solutions to PDEs with Gaussian initial conditions.

Provided mathematical framework for analyzing time-dependent random fields on the sphere.

Abstract

We construct time dependent random fields on the sphere through coordinates change and subordination and we study the associated angular power spectrum. Some of this random fields arise naturally as solutions of partial differential equations with random initial condition represented by a Gaussian random field.