Extreme Events and Event Size Fluctuations in Resetting Random Walks on Networks

Random walks with stochastic resetting, where walkers periodically return to a designated node, have emerged as an important framework for understanding transport processes in complex networks. While resetting is known to optimize search times, its effects on extreme events-defined as exceedances of walker flux above a critical threshold-remain largely unexplored. Such events model critical network phenomena, including traffic congestion, server overloads, and infrastructure failures. In this work, we systematically investigate how stochastic resetting influences both the probability and magnitude of extreme events in complex networks. Through analytical derivation of the stationary occupation probabilities and comprehensive numerical simulations, we demonstrate that resetting significantly reduces the occurrence of extreme events while concentrating event-size fluctuations. Our results reveal a universal suppression effect: increasing the resetting rate γ monotonically decreases extreme event probabilities across all nodes, with complete elimination at γ=1. Notably, this suppression is most pronounced for vulnerable low-degree nodes and nodes distant from the resetting node, which experience the largest reduction in both event probability and fluctuation magnitude. These findings provide theoretical foundations for using resetting as a control mechanism to mitigate extreme events in networked systems.