Self-healing percolation

We present a model of percolation inspired by the self-healing dynamics of a smart grid. Using a branching proess approximation, we find an analytical solution in the case of tree failures on random graphs. We then resort to numerical simulations to study planar lattices and find than in such cases duality plays a key role. Finally, we study the distribution of sites connected to a given source node and find the existence of two separate solutions that we study by applying cavity methods and recursive equations.