Antonio Scala — ISC-CNR Roma # 
Self Healing Percolation # 

We present a model of percolation mimicking the 
self-healing dynamics of a smart grid. While in the case of random graphs it is possible to work out an 
analytic solution, in the case of two dimensional networks we must resort to numerical simulations. Our 
findings hint that for planar lattices duality plays a key role yet to be understood. Finally, by to tackling 
the problem of being connected to a source node, we find the existence of two separate solutions that we study 
by applying cavity methods and recursive equations.