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In this chapter, we study the lower and upper H–S dimensions of the set \({\mathrm {X}}_{\zeta }( {\alpha })\) : \( \underline {\dim } \big ( \mathrm {X}_{\zeta } (\alpha ) \big )\) and \(\overline {\dim } \big ( \mathrm {X}_{\zeta } (\alpha )\big )\) . This is difficult in general, but we can estimate from below the dimension of this level set. In fact, we will study a more general level set. As an application, we study the relative multifractal formalism of a branching random walk on the Galton-Watson tree.

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

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  • 发表日期：

    2026年

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  • Najmeddine Attia,
  • Amal Mahjoub

摘要

In this chapter, we study the lower and upper H–S dimensions of the set \({\mathrm {X}}_{\zeta }( {\alpha })\) : \( \underline {\dim } \big ( \mathrm {X}_{\zeta } (\alpha ) \big )\) and \(\overline {\dim } \big ( \mathrm {X}_{\zeta } (\alpha )\big )\) . This is difficult in general, but we can estimate from below the dimension of this level set. In fact, we will study a more general level set. As an application, we study the relative multifractal formalism of a branching random walk on the Galton-Watson tree.