Multifractal analysis of random weak Gibbs measures

TL;DR

This paper investigates the multifractal properties of random weak Gibbs measures on attractors linked to $C^1$ random dynamics, establishing the multifractal formalism and calculating dimensions of level sets.

Contribution

It provides a comprehensive analysis of the multifractal structure of these measures, including dimension calculations and measure laws, in a random dynamical systems context.

Findings

Validity of the multifractal formalism for the measures.

Explicit calculation of Hausdorff and packing dimensions.

A 0-∞ law for measures of level sets.

Abstract

We describe the multifractal nature of random weak Gibbs measures on some class of attractors associated with $C^1$ random dynamics semi-conjugate to a random subshift of finite type. This includes the validity of the multifractal formalism, the calculation of Hausdorff and packing dimensions of the so-called level sets of divergent points, and a $0$-$\infty$ law for the Hausdorff and packing measures of the level sets of the local dimension.