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We introduce and study a vectorial multifractal formalism based on H–S measures, which parallels Peyrière’s multifractal framework using Hausdorff and packing measures. Additionally, we examine cases where the multifractal formalism fails to hold (Theorem A and Theorem B). As an application, we investigate the relative multifractal properties of branching random walks on Galton-Watson trees.

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A Relative Vectorial Multifractal Formalism of the Level Sets \(\mathrm {X}_{\zeta }(\alpha )\)

  • 章节

  • 发表日期：

    2026年

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  • Najmeddine Attia,
  • Amal Mahjoub

摘要

We introduce and study a vectorial multifractal formalism based on H–S measures, which parallels Peyrière’s multifractal framework using Hausdorff and packing measures. Additionally, we examine cases where the multifractal formalism fails to hold (Theorem A and Theorem B). As an application, we investigate the relative multifractal properties of branching random walks on Galton-Watson trees.