Sulzbach, Henning A functional limit law for the profile of plane-oriented recursive trees. (English) Zbl 1355.05229 Fifth colloquium on mathematics and computer science. Lectures from the colloquium, Blaubeuren, Germany, September 22–26, 2008. Nancy: The Association. Discrete Mathematics & Theoretical Computer Science (DMTCS). Discrete Mathematics and Theoretical Computer Science Proceedings AI, 339-350 (2008). Summary: We give a functional limit law for the normalized profile of random plane-oriented recursive trees. The proof uses martingale convergence theorems in discrete and continuous-time. This complements results of H.-K. Hwang [Random Struct. Algorithms 30, No. 3, 380–413 (2007; Zbl 1115.05083)].For the entire collection see [Zbl 1172.05004]. Cited in 5 Documents MSC: 05C80 Random graphs (graph-theoretic aspects) 05C05 Trees 60C05 Combinatorial probability 60F17 Functional limit theorems; invariance principles 68P05 Data structures Keywords:plane-oriented recursive trees; random trees; profile of trees; preferential attachment; branching random walk; martingales; analysis of algorithms PDF BibTeX XML Cite \textit{H. Sulzbach}, in: Fifth colloquium on mathematics and computer science. Lectures from the colloquium, Blaubeuren, Germany, September 22--26, 2008. Nancy: The Association. Discrete Mathematics \& Theoretical Computer Science (DMTCS). 339--350 (2008; Zbl 1355.05229) Full Text: Link