Physics-Inspired Diffusion Models for Social Influence: Beyond Local and Markovian Assumptions

Current influence models often assume local, memoryless spread (e.g., Bin Xiang et al., 2024), but many social processes involve long-term dependencies or non-local jumps (think rumors resurfacing years later or cross-community "jumps"). Drawing from physics—like fractional diffusion, percolation theory, or models with memory effects—this work would develop and empirically validate new diffusion models for social networks that incorporate these features. For instance, one could adapt the hyperparametric IC model to allow for delayed or reactivated influence, or for "super-spreader" links that bypass standard network topology. This approach explicitly challenges the Markovian/locality assumptions that dominate current SNA, opening the door to richer, more realistic models with direct applications to viral content, rumor resurgence, and even meme culture. It’s a clear extension and challenge to models like those in Bin Xiang et al. (2024) and Zhu et al. (2021).

References:

1. Predicting Cascading Failures with a Hyperparametric Diffusion Model. Bin Xiang, Bogdan Cautis, Xiaokui Xiao, Olga Mula, D. Niyato, L. Lakshmanan (2024). Knowledge Discovery and Data Mining.
2. A Local Search Algorithm for the Influence Maximization Problem. Enqiang Zhu, Lidong Yang, Yuguang Xu (2021). Frontiers of Physics.