Asymptotics of multifractal products of spherical random fields

TL;DR

This paper develops new limit theorems for multifractal measures on the sphere, broadening the understanding of their asymptotic behavior and multifractal properties under general conditions.

Contribution

It introduces generalized limit theorems for multifractal products of spherical fields, allowing for broader classes of fields and more flexible multifractal measures.

Findings

Established new limit theorems under general mixing conditions.

Derived the Réný function for the limiting measure.

Provided conditions for non-degeneracy of the limit measure.

Abstract

The paper studies multifractal random measures on the sphere $\mathbb{S}^d$ constructed via multifractal products of random fields. It presents new limit theorems for multifractal products of spherical fields and conditions for the non-degeneracy of the limiting measure. The multifractal properties of the limiting measure are investigated, and its R\'enyi function is derived. Compared to earlier results on multifractal products of spherical fields, the obtained limit theorems hold under general mixing conditions, enabling the consideration of multifractal products of fields from a broad class and the construction of random measures with flexible multifractal properties.