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On the multifractal analysis of the covering number on the Galton–Watson tree
Journal article   Peer reviewed

On the multifractal analysis of the covering number on the Galton–Watson tree

Najmeddine Attia
Journal of applied probability, Vol.56(1), pp.265-281
03/2019
DOI: https://doi.org/10.1017/jpr.2019.17

Abstract

Research Papers
We consider, for t in the boundary of a Galton–Watson tree $(\partial \textsf{T})$, the covering number $(\textsf{N}_n(t))$ by the generation-n cylinder. For a suitable set I and sequence (sn), we almost surely establish the Hausdorff dimension of the set $\{ t \in \partial {\textsf{T}}:{{\textsf{N}}_n}(t) - nb \ {\sim} \ {s_n}\} $ for b ∈ I.

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