Capannoli, F., & den Hollander, F. (2024). Interacting Particle Systems on Random Graphs. arXiv preprint arXiv:2410.17766.
This paper provides a comprehensive overview of the behavior of Interacting Particle Systems (IPS) on random graphs, focusing on three key models: the Stochastic Ising Model (SIM), the Voter Model (VM), and the Contact Process (CP). The authors aim to highlight the key differences in behavior observed in these models when applied to various random graph structures, emphasizing the impact of graph sparsity and density.
The paper presents a structured overview of the topic, starting with a general introduction to IPS on the infinite lattice Z^d. It then delves into the specifics of SIM, VM, and CP on finite random graphs, including the Erdős-Rényi Random Graph, Configuration Model, and Preferential Attachment Model. The authors utilize mathematical definitions, theorems, and illustrative examples to explain the concepts and key findings.
The study of IPS on random graphs is a rapidly developing field with numerous open questions. The authors emphasize the importance of understanding the interplay between graph structure, system dynamics, and time scales in determining the critical behavior of these models.
This overview provides valuable insights into the complexities of IPS on random graphs, highlighting the need for further research in this area. Understanding the behavior of these models on different graph structures has implications for various fields, including statistical physics, network science, and social dynamics.
The paper primarily focuses on theoretical aspects of IPS on random graphs. Further research is needed to explore the practical implications and applications of these models in real-world networks. Additionally, investigating the behavior of other IPS models on random graphs could provide further insights into the interplay between network topology and system dynamics.
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by F. Capannoli... at arxiv.org 10-24-2024
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