Limit distribution of degrees in random family trees

TL;DR

This paper investigates the asymptotic degree distribution of vertices in a class of random trees, including the Barabasi-Albert model, using Polya urn techniques to analyze their limiting behavior.

Contribution

It provides new insights into the degree distribution in random family trees, extending existing models with rigorous asymptotic analysis.

Findings

Almost sure degree behavior characterized

Limiting degree distribution derived

Applicable to Barabasi-Albert and similar models

Abstract

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. Results about Polya urn models are applied in the proofs.