Free deformations of a random spring network

We discuss some properties of the phase occurring in between the connectivity percolation threshold and the rigidity one, for a randomly diluted lattice of springs. We introduce a domain of free extension, which separates the floppy regime from the elastic one in the dilution case. We mention, in particular, the equivalent problem for the randomly reinforced spring network, the connection with the splay-rigid regime and the occurrence of walls inside the domain of free displacements.