Contact matrices provide a coarse grained description of the configurationω of a linear chain (polymer or random walk) on Z: Cij (ω) = 1 when the distance between the positions of the ith and j th steps are less than or equal to some distance a and Cij (ω) = 0 otherwise. We consider models in which polymers of length N have weights corresponding to simple and self-avoiding random walks, SRW and...