Self Healing Percolation

We introduce the concept of self-healing in distribution networks characterised by a flow of services. We define the problem in terms of a distributed message-passing protocol that we analise both with numerical simulations and with the cavity method. We find that the system is subject to two kind of events: major blackouts and percolative healing. We then generalise the model to a percolation problem that we solve in the case of Erdos-Renyii networks on the complete graph; furthermore, we analyse the two dimensional behavior via numerical simulations. We find that, like in standard 2d percolation, duality rules the transition lines of self-healing percolation on planar lattices.