2020/02/28 by Bas Lodewijks, Marcel Ortgiese, Lodewijks, Bas +1
Mathematics · Physics and Astronomy · Social Sciences · #Complex Network Analysis Techniques #Evolutionary Game Theory and Cooperation #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR
paper · pdf · doi:10.48550/arxiv.2002.12863
48 pages
openalex publication_date 2020/02/28 · arxiv created 2020/03/20 · arxiv updated 2020/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Preferential attachment models form a popular class of growing networks, where incoming vertices are preferably connected to vertices with high degree. We consider a variant of this process, where vertices are equipped with a random initial fitness representing initial inhomogeneities among vertices and the fitness influences the attractiveness of a vertex in an additive way. We consider a heavy-tailed fitness distribution and show that the model exhibits a phase transition depending on the tail exponent of the fitness distribution. In the weak disorder regime, one of the old vertices has maximal degree irrespective of fitness, while for strong disorder the vertex with maximal degree has to satisfy the right balance between fitness and age. Our methods use martingale methods to show concentration of degree evolutions as well as extreme value theory to control the fitness landscape.