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

Abstract

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

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Acknowledgements

The author thanks Professor Julien Barral for suggesting the idea of this work. He also thanks the anonymous referees for their valuable comments and suggestions that led to improvement of the manuscript.

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Correspondence to Najmeddine Attia.

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Attia, N. On the Multifractal Analysis of Branching Random Walk on Galton–Watson Tree with Random Metric. J Theor Probab 34, 90–102 (2021). https://doi.org/10.1007/s10959-019-00984-z

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Keywords

  • Galton–Watson tree
  • Random walk
  • Hausdorff and packing dimensions

Mathematics Subject Classification (2010)

  • 60G50
  • 11K55