Exploring Random Walks on Networks: An analysis of Extreme Events

Abstract

With its key role in our modern lives, understanding transportation systems and mobility from scientific frameworks is vital to designing more resilient and robust systems of travel. In contrast to the conventional approach of looking at complex models directly, we promote building up from simpler models that are more interpretable to more realistic models. We also additionally realize the multimodal nature of transportation and transit and the crucial role it plays in future developments. Using the rich analytical vocabulary of network science, we decide to investigate the behavior of simple random walks on multilayer networks. Inspired by previous works in the area, we enquire especially regarding the evolution and propagation of extreme events that are borne out of such dynamics. We further introduce features into the random walk dynamics to track new sources of extreme behavior. We also explore the phenomena of non-markovian random walks so as to enquire about its implications on the occurrence of extreme events. We see the consistent occurrence of extreme events when extended to multilayer networks and also in random walks with rerouting strategies. We uncover sudden transitions in the states of the networks in random walks with cascades and a decreasing influence of adding memory on the occurrence of extreme events. Our study demonstrates the importance of this modeling approach to understand real-world dynamics on networks and opens up several avenues to further explore this and an opportunity to pair it with data-based approaches