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Localized perturbations in a real-world network have the potential to triggercascade failures at the whole system level, hindering its operations andfunctions. Standard approaches analytically tackling this problem are mostlybased either on static descriptions, such as percolation, or on models wherethe failure evolves through first-neighbor connections, crucially failing tocapture the nonlocal behavior typical of real cascades. We introduce adynamical model that maps the failure propagation across the network to aself-avoiding random walk that, at each step, has a probability to performnonlocal jumps toward operational systems' units. Despite the inherentnon-Markovian nature of the process, we are able to characterize the criticalbehavior of the system out of equilibrium, as well as the stopping timedistribution of the cascades. Our numerical experiments on synthetic andempirical biological and transportation networks are in excellent agreementwith theoretical expectation, demonstrating the ability of our framework toquantify the vulnerability to nonlocal cascade failures of complex systems withinterconnected structure.

Non-Markovian random walks characterize network robustness to nonlocal cascades