Geodesic
Note on the Multifractal Formalism of Covering Number on the Galton-Watson Tree
Kragujevac Journal of Mathematics, Tome 49 (2025) no. 1, p. 43

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We consider, for $t$ in the boundary of Galton-Watson tree ($\partial\mathsf T$), the covering number ${\mathsf N_n(t)}$ by cylinder of generation $n$. For a suitable set $I$ and a sequence $(s_{n,\gamma})$, we establish almost surely, and uniformly on $\gamma$, the Hausdorff and packing dimensions of the set $\{t\in\partial\mathsf T:{\mathsf N}_n(t)-nb\sim s_{n,\gamma}\}$ for $b\in I$.
Classification : 60G50, 28A78
Keywords: random covering, Hausdorff dimension, indexed martingale, Galton-Watson tree 
Najmedine Attia; Meriem Ben Hadj Khalifa. Note on the Multifractal Formalism of Covering Number on the Galton-Watson Tree. Kragujevac Journal of Mathematics, Tome 49 (2025) no. 1, p. 43 . http://geodesic.mathdoc.fr/item/KJM_2025_49_1_a3/
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