Sparsity for isotropic spherical random fields

TL;DR

This paper presents a new sparse representation for isotropic spherical random fields that enables efficient simulation, mimics complex spectral properties, and maintains isotropy, addressing key challenges in cosmology.

Contribution

It introduces a simple sparse representation for isotropic spherical fields that can replicate spectral features and preserve isotropy, with applications in efficient simulation and cosmology.

Findings

Sparse representation effectively mimics angular power spectrum and polyspectra.

Proposed methods enable computationally efficient simulation algorithms.

Sparse approximations preserve isotropy in spherical random fields.

Abstract

We introduce a simple representation for isotropic spherical random fields and we discuss how it allows to discuss different notions of sparsity under isotropy. We also show how a suitable construction of sparse fields can mimic well the angular power spectrum and the polyspectra of some popular non-Gaussian fields, at the same time allowing for computationally efficient simulation algorithms. Using related ideas we also show how it is possible to obtain sparse approximations of spherical random fields which preserve isotropy, thus addressing an issue which has been raised in the Cosmological literature.