2024/09/16 by Sayan Banerjee, Banerjee, Sayan, Shankar Bhamidi +5
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Probability (math.PR) #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2409.10307
openalex publication_date 2024/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Owing to the influence of real-world networks both in science and society, numerous mathematical models have been developed to understand the structure and evolution of these systems, particularly in a temporal context. Recent advancements in fields like distributed cyber-security and social networks have spurred the creation of probabilistic models of evolution, where individuals make decisions based on only partial information about the network's current state. This paper seeks to explore models incorporating network delay, where new participants receive information from a time-lagged snapshot of the system. In the context of mesoscopic network delays, we develop probabilistic tools built on stochastic approximation to understand asymptotics of both local functionals, such as local neighborhoods and degree distributions, as well as global properties, such as the evolution of the degree of the network's initial founder. A companion paper explores the regime of macroscopic delays in the evolution of the network.