2004/10/25 by Anna Rudas, Rudas, Anna
Mathematics · #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR
paper · pdf · doi:10.48550/arxiv.math/0410532
17 pages, no figures, submitted to Random Structures and Algorithms
arxiv created 2004/10/25 · openalex publication_date 2004/10/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend the results of B. Bollobas, O. Riordan, J. Spencer, G. Tusnady, and Mori. We consider a model of random tree growth, where at each time unit a new node is added and attached to an already existing node chosen at random. The probability with which a node with degree k is chosen is proportional to w(k), where w is a fixed weight function. We prove that if w fulfills some asymptotic requirements then the degree sequence converges in probability, we give the limit. In particular if w is asymptotically linear then the degree sequence decays with power law. Our method of proof is analytic rather than combinatorial, having the advantage of robustness: only asymptotic properties of the weight function w are used, while in the cited papers the explicit law w(k)=ak+b is assumed.