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Suppose that μ is the branching measure on the boundary of a supercritical Galton-Watson tree with offspring distribution N such that E[Nlog + N]<~. We determine the dimension spectrum of thin points under the condition P{N=<1}=0 and the dimension spectrum of thick points under the condition that either 0<sup{t:E[exp(tN)]<~}<~ or ess supN<~. Our main tool for obtaining lower...
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