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.
"Limit distribution of degrees in random family trees." Electron. Commun. Probab. 16 29 - 37, 2011. https://doi.org/10.1214/ECP.v16-1598