Geiger, Jochen Poisson point process limits in size-biased Galton-Watson trees. (English) Zbl 0963.60084 Electron. J. Probab. 5, Paper No. 17, 12 p. (2000). Let \(Z_t\), \(t\geq 0,\) be a continuous-time critical binary Galton-Watson branching process starting with a single founding ancestor, and let \(\widehat{T}_t\) be the tree of the process size-biased according to the number of particles at time \(t.\) By keeping track of 1) the times when different families grow out of the distinguished line of descent of a particle picked at random among existing at time \(t,\) 2) the sizes of the respective families at time \(t,\) the author constructs a point process in a time-size plane and studies its properties for the cases of single-type and some multi-type continuous-time Galton-Watson processes. As a corollary, he shows in particular, that the number of edges of height \(t\) in \(\widehat{T}_t\) has a gamma limit law with shape parameter 2. Reviewer: Vladimir Vatutin (Moskva) Cited in 4 Documents MSC: 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) 60G55 Point processes (e.g., Poisson, Cox, Hawkes processes) Keywords:Galton-Watson process; random tree; limit laws PDFBibTeX XMLCite \textit{J. Geiger}, Electron. J. Probab. 5, Paper No. 17, 12 p. (2000; Zbl 0963.60084) Full Text: DOI EuDML EMIS