Thin and thick points for branching measure on a Galton-Watson tree
The authors consider a supercritical Galton-Watson tree starting from a single progenitor, with offspring distribution \(N\) such that \(E[N\log^+ N]<\infty\). They obtain the dimension spectrum when \(P\{N \leq 1 \}=0\), and when \(0\), \(\sup\{t: E[\exp(tN)]<\infty\}<\infty\). These generalize the results of \textit{N.-R. Shieh} and \textit{S. J. Taylor} [Stochastic Processes Appl. 75, No. 2, 249-261 (1998; Zbl 0932.60041)] and \textit{Q. Liu} [Ann. Inst. Henri Poincaré, Probab. Stat. 37, No. 2, 195-222 (2001; Zbl 0986.60080)].
scientific article; zbMATH DE number 1796759