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
• DOI: 10.1016/s0167-7152(02)00093-7

✦ 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.