Talk - Scaling Limits in Spatial Birth-Death Systems with Long-Range Interactions
Abstract
In this talk, we examine the interaction graph of a novel bipartite spatial birth-death particle system characterized by long-range interactions and heavy-tailed degree distributions. Studying such models is crucial for understanding complex systems, such as scientific collaboration networks. In our model, we represent authors as entities with exponentially distributed lifetimes and papers as timestamped events. Furthermore, regularly varying weights assigned to both authors and papers influence their spatial interaction range, resulting in a dynamic spatial interaction graph. In the large-system limit, we show that, depending on the tail index of the author–paper degree distribution, the scaling limit of the normalized author–paper edge count is a Gaussian autoregressive process in regimes with lighter tails, and a non-Markovian alpha-stable process in the heavy-tailed case.
