  Recent progress in extremely correlated Fermi liquid theory (ECFL) and
dynamical mean field theory (DMFT) enables us to compute in the $d \to \infty$
limit the resistivity of the $t-J$ model after setting $J\to0$. This is also
the $U=\infty$ Hubbard model. We study three densities $n=.75,.8,.85$ that
correspond to a range between the overdoped and optimally doped Mott insulating
state. We delineate four distinct regimes characterized by different behaviors
of the resistivity $\rho$. We find at the lowest $T$ a Gutzwiller Correlated
Fermi Liquid regime with $\rho \propto T^2$ extending up to an effective Fermi
temperature that is dramatically suppressed from the non-interacting value.
This is followed by a Gutzwiller Correlated Strange Metal regime with $\rho
\propto (T-T_0)$, i.e. a linear resistivity extrapolating back to $\rho=0$ at a
positive $T_0$. At a higher $T$ scale, this crosses over into the Bad Metal
regime with $\rho \propto (T+T_1)$ extrapolating back to a finite resistivity
at $T=0$, and passing through the Ioffe-Regel-Mott value where the mean free
path is a few lattice constants. This regime finally gives way to the High $T$
Metal regime, where we find $\rho \propto T$. The present work emphasizes the
first two, where the availability of an analytical ECFL theory is of help in
identifying the changes in related variables entering the resistivity formula
that accompany the onset of linear resistivity, and the numerically exact DMFT
helps to validate the results. We also examine thermodynamic variables such as
the magnetic susceptibility, compressibility, heat capacity and entropy, and
correlate changes in these with the change in resistivity. This exercise casts
valuable light on the nature of charge and spin correlations in the strange
metal regime, which has features in common with the physically relevant strange
metal phase seen in strongly correlated matters.
