  We study the joint statistics of conductance $G$ and shot noise $P$ in
chaotic cavities supporting a large number $N$ of open electronic channels in
the two attached leads. We determine the full phase diagram in the $(G,P)$
plane, employing a Coulomb gas technique on the joint density of transmission
eigenvalues, as dictated by Random Matrix Theory. We find that in the region of
typical fluctuations, conductance and shot noise are uncorrelated and jointly
Gaussian, and away from it they fluctuate according to a different joint rate
function in each phase of the $(G,P)$ plane. Different functional forms of the
rate function in different regions emerge as a direct consequence of third
order phase transitions in the associated Coulomb gas problem.
