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Limit distribution of degrees in random family trees. (English) Zbl 1228.05242
Summary: In a one-parameter model for evolution of random trees, which also includes the Barabasi-Albert random tree, almost sure behavior and the limiting distribution of the degree of a vertex in a fixed position are examined. A functional central limit theorem is also given. Results about Polya urn models are applied in the proofs.

MSC:
05C75 Structural characterization of families of graphs
05C05 Trees
05C80 Random graphs (graph-theoretic aspects)
60C05 Combinatorial probability
60F15 Strong limit theorems
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