that we are aiming to investigate \[cf. the discussion at the end of Sec. \[SEC:FTMF\]\].

From the discussion above, the RLPM is a convenient minimal model of soft random solids, inasmuch as it adequately captures the necessary long-wavelength physics. It can be regarded as either a model of a chemical gel, or as a caricature of vulcanized rubber or other soft random solid. The RLPM can be viewed as a simplified version of vulcanization theory [@Castillo1994; @Goldbart2004], with microscopic details, such as polymer chain conformations, being ignored. Nevertheless, it is able to reproduce the same universality class as vulcanization theory at the liquid-to-random-solid transition. For the study of elasticity, we shall consider length-scales on which the system is a well-defined solid (i.e., scales longer than the localization length, as we shall see later in this paper). Both of these scales are much larger than the characteristic linear dimension of an individual polymer. The RLPM is a model very much in the spirit of lattice percolation, except that it naturally allows for particle motion as well as particle connectivity, and is therefore suitable for the study of continuum elasticity and other issues associated with the (thermal or deformational) motion of the 