On the multifractal analysis of the covering number on the Galton–Watson tree
AbstractWe 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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2010 ◽
Vol 10
(01)
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pp. 53-75
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2015 ◽
Vol 35
(8)
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pp. 2559-2586
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2009 ◽
Vol 29
(1)
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pp. 73-109
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