Large deviation theory of percolation on multiplex networks

Recently, increasing attention has been paid to the fluctuations observed in percolation defined in single and multiplex networks. These fluctuations are extremely important to characterize the robustness of real finite networks but cannot be captured by the traditionally adopted mean-field theory of percolation. Here we propose a theoretical framework and a message passing algorithm that is able to fully capture the large deviation of percolation in interdependent multiplex networks with a locally tree-like structure. This framework is here applied to study the robustness of single instance multiplex networks and compared to the results obtained using extensive simulations of the initial damage. For simplicity the method is here developed for interdependent multiplex networks without link overlap, however it can be generalized to treat multiplex networks with link overlap.