  We study the interactions between the coherent quasiparticles and the
incoherent Mott-Hubbard excitations and their effects on the low energy
properties in the $U=\infty$ Hubbard model. Within the framework of a
systematic large-N expansion, these effects first occur in the next to leading
order in 1/N. We calculate the scattering phase shift and the free energy, and
determine the quasiparticle weight Z, mass renormalization, and the
compressibility. It is found that the compressibility is strongly renormalized
and diverges at a critical doping $\delta_c=0.07\pm0.01$. We discuss the nature
of this zero-temperature phase transition and its connection to phase
separation and superconductivity.
