Extreme events in stochastic transport on networks

Abstract

Extreme events are emergent phenomena in multi-particle transport processes on complex networks. In practice, such events could range from power blackouts to call drops in cellular networks to traffic congestion on roads. All the earlier studies of extreme events on complex networks have focused only on the nodal events. If random walks are used to model transport process on a network, it is known that degree of the nodes determines the extreme event properties. In contrast, in this work, it is shown that extreme events on the edges display a distinct set of properties from that of the nodes. It is analytically shown that the probability for the occurrence of extreme events on an edge is independent of the degree of the nodes linked by the edge and is dependent only on the total number of edges on the network and the number of walkers on it. Further, it is also demonstrated that non-trivial correlations can exist between the extreme events on the nodes and the edges. These results are in agreement with the numerical simulations on synthetic and real-life networks.

References in corpus (17)

• Catastrophic cascade of failures in interdependent networks
• Statistical physics of social dynamics
• The large deviation approach to statistical mechanics
• Statistical physics of human cooperation
• Recommender Systems
• Statistical physics of vaccination
• Statistical physics of crime: A review
• Introduction to dynamical large deviations of Markov processes
• Network dynamics of innovation processes
• Return interval distribution of extreme events and long term memory
• Effective interactions and large deviations in stochastic processes
• Extreme events on complex networks
• Knowledge Acquisition: A Complex Networks Approach
• Extreme events and event size fluctuations in biased random walks on networks
• Manipulation of extreme events on scale-free networks
• Reactive random walkers on complex networks
• Random Walks on Complex Networks

Cited by in corpus (8)

• Extreme events in dynamical systems and random walkers: A review
• Extreme events in globally coupled chaotic maps
• Emergence of extreme events in a quasi-periodic oscillator
• First detection of threshold crossing events under intermittent sensing
• Biased random walkers and extreme events on the edges of complex networks
• Dynamical fluctuations of random walks in higher-order networks
• Maximal dispersion of adaptive random walks
• Continuous Gated First-Passage Processes