  In this paper we analyse both the dynamics and the high density physics of
the infinite dimensional lattice gas model for random heteropolymers recently
introduced in \cite{jort}. Restricting ourselves to site-disordered
heteropolymers, we derive exact closed deterministic evolution equations for a
suitable set of dynamic order parameters (in the thermodynamic limit), and use
these to study the dynamics of the system for different choices of the monomer
polarity parameters. We also study the equilibrium properties of the system in
the high density limit, which leads to a phase diagram exhibiting transitions
between swollen states, compact states, and regions with partial
compactification. Our results find excellent verification in numerical
simulations, and have a natural and appealing interpretation in terms of real
heteropolymers.
