Year: 2025
Type: article
Abstract: ABSTRACT 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 (Banerjee et al. 2024) explores the regime of macroscopic delays in the evolution of the network.
Source: Random Structures and Algorithms
DOI: 10.1002/rsa.70029
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,550
Awards: Network Time Series: From Dynamics to Coevolution, Mathematical Sciences Research Institute (MSRI), NSF-SNSF: Functional data analysis for complex systems, G329468232, CAREER: Network Centrality and Its Applications in Detection, Dynamics, and Load Balancing, RTG: Networks: Foundations in Probability, Optimization, and Data Sciences, G6019427330, Collaborative Research: Network Analysis via Optimal Transport of Markov Embeddings, G6671297155
OpenAlex ID: W4413961692