Extreme events and event size fluctuations in biased random walks on networks

Abstract

Random walk on discrete lattice models is important to understand various types of transport processes. The extreme events, defined as exceedences of the flux of walkers above a prescribed threshold, have been studied recently in the context of complex networks. This was motivated by the occurrence of rare events such as traffic jams, floods, and power black-outs which take place on networks. In this work, we study extreme events in a generalized random walk model in which the walk is preferentially biased by the network topology. The walkers preferentially choose to hop toward the hubs or small degree nodes. In this setting, we show that extremely large fluctuations in event-sizes are possible on small degree nodes when the walkers are biased toward the hubs. In particular, we obtain the distribution of event-sizes on the network. Further, the probability for the occurrence of extreme events on any node in the network depends on its 'generalized strength', a measure of the ability of a node to attract walkers. The 'generalized strength' is a function of the degree of the node and that of its nearest neighbors. We obtain analytical and simulation results for the probability of occurrence of extreme events on the nodes of a network using a generalized random walk model. The result reveals that the nodes with a larger value of 'generalized strength', on average, display lower probability for the occurrence of extreme events compared to the nodes with lower values of 'generalized strength'.

References in corpus (7)

• Dynamics of jamming transitions in complex networks
• Congestion phenomena on complex networks
• Maximal-entropy random walks in complex networks with limited information
• Scaling breakdown in flow fluctuations on complex networks
• Extreme events on complex networks
• Localization Transition of Biased Random Walks on Random Networks
• Random Walks on Complex Networks

Cited by in corpus (18)

• Extreme events in dynamical systems and random walkers: A review
• Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model
• Diffusions conditioned on occupation measures
• Convergence of large deviation estimators
• A probabilistic decomposition-synthesis method for the quantification of rare events due to internal instabilities
• Large deviations of random walks on random graphs
• Mean encounter times for multiple random walkers on networks
• Generalized optimal paths and weight distributions revealed through the large deviations of random walks on networks
• Manipulation of extreme events on scale-free networks
• Extreme events in stochastic transport on networks
• Dynamical phase transition in the occupation fraction statistics for non-crossing Brownian particles
• Optimal exploration of random walks with local bias on networks
• Biased random walkers and extreme events on the edges of complex networks
• Balanced condition in networks leads to Weibull statistics
• Dynamical fluctuations of random walks in higher-order networks
• Maximal dispersion of adaptive random walks
• A measure of dissimilarity between diffusive processes on networks
• Rare events statistics of random walks on networks: localization and other dynamical phase transitions