include chemical gels [@Addad1996], which are formed by the permanent random chemical bonding of small molecules, as well as rubber [@Treloar1975], which is formed via the introduction of permanent random chemical cross-links between nearby monomers in melts or solutions of flexible long-chain polymers. Soft random solids are characterized by their *entropic elasticity*. These are media in which the shear modulus originates in the strong thermal fluctuations of the configurations of the constituent particles and is much smaller than the bulk modulus, which is energetic in nature and originates in the excluded-volume interactions between the particles. The concept of entropic elasticity forms the basis of the classical theory of rubber elasticity, developed long ago by Kuhn, Flory, Wall, Treloar and others (see Ref. [@Treloar1975]).

As we discuss soft random solids we shall take chemical gels as our prototype media. When the density of the introduced links exceeds the percolation threshold, an infinite cluster of linked molecules forms, spanning the system, and the network acquires a thermodynamic rigidity with respect to shear deformations [^1]. This event is often called the gelation transition or the vulcanization transition [@Goldbart1996].

The [*geometrical*]{} or [*architectural*]{} aspects of the gelation/vulcanization transition can be well captured by the 