Rare events and discontinuous percolation transitions

Abstract

Percolation theory characterizing the robustness of a network has applications ranging from biology, to epidemic spreading, and complex infrastructures. Percolation theory, however, only concern the typical response of a infinite network to random damage of its nodes while in real finite networks, fluctuations are observable. Consequently for finite networks there is an urgent need to evaluate the risk of collapse in response to rare configurations of the initial damage. Here we build a large deviation theory of percolation characterizing the response of a sparse network to rare events. This general theory includes the second order phase transition observed typically for random configurations of the initial damage but reveals also discontinuous transitions corresponding to rare configurations of the initial damage for which the size of the giant component is suppressed.

(11 pages, 4 figures)

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• Large deviation theory of percolation on multiplex networks
• Percolation on branching simplicial and cell complexes and its relation to interdependent percolation
• Large deviations of random walks on random graphs
• Smeared phase transitions in percolation on real complex networks
• Renormalization group for link percolation on planar hyperbolic manifolds
• Impact of presymptomatic transmission on epidemic spreading in contact networks: A dynamic message-passing analysis
• Generalized optimal paths and weight distributions revealed through the large deviations of random walks on networks
• Heterogeneous message passing for heterogeneous networks
• Statistical mechanics of bipartite $z$-matchings
• Dynamical fluctuations of random walks in higher-order networks
• Scaling relations and finite-size scaling in gravitationally correlated lattice percolation models
• Maximal dispersion of adaptive random walks
• Percolation Transitions in Growing Networks Under Achlioptas Processes: Analytic Solutions
• Heterogeneity in Outcomes of Repeated Instances of Percolation Experiments
• On the accuracy of message-passing approaches to percolation in complex networks
• Phase transitions in atypical systems induced by a condensation transition on graphs
• Large deviation and anomalous fluctuations scaling in degree assortativity on configuration networks
• Efficient message passing for cascade size distributions on finite trees
• Anomalous percolation transitions beyond the BKT transition in growing networks