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Thin and thick points for branching measure on a Galton–Watson tree

✍ Scribed by Peter Mörters; Narn-Rueih Shieh


Book ID
104301872
Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
133 KB
Volume
58
Category
Article
ISSN
0167-7152

No coin nor oath required. For personal study only.

✦ Synopsis


Suppose that

is the branching measure on the boundary of a supercritical Galton-Watson tree with o spring distribution N such that E[N log + N ] ¡ ∞. We determine the dimension spectrum of thin points under the condition P{N 6 1} = 0 and the dimension spectrum of thick points under the condition that either 0 ¡ sup{t: E[exp(tN )] ¡ ∞} ¡ ∞ or ess sup N ¡ ∞. Our main tool for obtaining lower bounds is to study percolation on the Galton-Watson tree.


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