2006/08/09 by Konstantin Borovkov, Vladimir Vatutin, Borovkov, Konstantin +1
Mathematics · Physics and Astronomy · #05C05 #05C80 (primary) #60F99 (secondary) #60G50 #Binary tree #Combinatorics #Complex Network Analysis Techniques #Computer science #Discrete mathematics #FOS: Mathematics #Geometry #Graph #Independent and identically distributed random variables #Infinity #Mathematical analysis #Mathematics #Probability (math.PR) #Product (mathematics) #Random binary tree #Random graph #Random tree #Random variable #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Tree (set theory) #Vertex (graph theory) #math.PR #msc:05C05 #msc:05C80 #msc:60F99 #msc:60G50
paper · pdf · doi:10.48550/arxiv.math/0608211
26 pages
arxiv created 2006/08/09 · openalex publication_date 2006/08/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider growing random recursive trees in random environment, in which at each step a new vertex is attached (by an edge of a random length) to an existing tree vertex according to a probability distribution that assigns the tree vertices masses proportional to their random weights. The main aim of the paper is to study the asymptotic behaviour of the distance from the newly inserted vertex to the tree's root and that of the mean numbers of outgoing vertices as the number of steps tends to infinity. Most of the results are obtained under the assumption that the random weights have a product form with independent identically distributed factors.