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On the Multifractal Analysis of Branching Random Walk on Galton–Watson Tree with Random Metric

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  • Najmeddine Attia

    (Faculté des Sciences de Monastir)

Abstract

We consider a branching random walk $$S_nX(t)$$ S n X ( t ) on a supercritical random Galton–Watson tree. We compute the Hausdorff and packing dimensions of the level set $$E(\alpha )$$ E ( α ) of infinite branches in the boundary of tree endowed with random metric along which the average of $$S_n X(t)/n$$ S n X ( t ) / n have a given limit point.

Suggested Citation

  • Najmeddine Attia, 2021. "On the Multifractal Analysis of Branching Random Walk on Galton–Watson Tree with Random Metric," Journal of Theoretical Probability, Springer, vol. 34(1), pages 90-102, March.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:1:d:10.1007_s10959-019-00984-z
    DOI: 10.1007/s10959-019-00984-z
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    References listed on IDEAS

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    1. Julien Barral, 2000. "Continuity of the Multifractal Spectrum of a Random Statistically Self-Similar Measure," Journal of Theoretical Probability, Springer, vol. 13(4), pages 1027-1060, October.
    2. Najmeddine Attia, 2014. "On the Multifractal Analysis of the Branching Random Walk in $$\mathbb{R }^d$$ R d," Journal of Theoretical Probability, Springer, vol. 27(4), pages 1329-1349, December.
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    Cited by:

    1. Mahjoub, Amal & Attia, Najmeddine, 2022. "A relative vectorial multifractal formalism," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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