  Localized perturbations in a real-world network have the potential to trigger
cascade failures at the whole system level, hindering its operations and
functions. Standard approaches analytically tackling this problem are mostly
based either on static descriptions, such as percolation, or on models where
the failure evolves through first-neighbor connections, crucially failing to
capture the nonlocal behavior typical of real cascades. We introduce a
dynamical model that maps the failure propagation across the network to a
self-avoiding random walk that, at each step, has a probability to perform
nonlocal jumps toward operational systems' units. Despite the inherent
non-Markovian nature of the process, we are able to characterize the critical
behavior of the system out of equilibrium, as well as the stopping time
distribution of the cascades. Our numerical experiments on synthetic and
empirical biological and transportation networks are in excellent agreement
with theoretical expectation, demonstrating the ability of our framework to
quantify the vulnerability to nonlocal cascade failures of complex systems with
interconnected structure.
