  Using trajectories from acoustically tracked (RAFOS) floats in the Gulf of
Mexico, we construct a geography of its Lagrangian circulation within the
1500--2500-m layer. This is done by building a Markov-chain representation of
the Lagrangian dynamics. The geography is composed of weakly interacting
provinces that constrain the connectivity at depth. The main geography includes
two provinces of near equal areas and separated by a roughly meridional
boundary. The residence time is about 4.5 (3.5) years in the western (eastern)
province. The exchange between these provinces is effected through a slow
cyclonic circulation, which is well constrained in the western basin by
preservation of $f/H$, where $f$ is the Coriolis parameter and $H$ is depth.
Secondary provinces of varied shapes covering smaller areas are identified with
residence times ranging from about 0.4 to 1.2 years or so. Except for the main
provinces, the deep Lagrangian geography does not resemble the surface
Lagrangian geography recently inferred from satellite-tracked drifter
trajectories. This implies disparate connectivity characteristics with
potential implications for pollutant (e.g., oil) dispersal at the surface and
depth. A ventilation conduit through the southeastern corner of the domain from
the Caribbean Sea balanced by weak vertical exchange is also inferred. This is
supported by the inspection of satellite-tracked profiling (Argo) floats,
which, while forming a smaller dataset and having seemingly different
water-following characteristics than the RAFOS floats, replicate the main
aspects of the Lagrangian geography. Finally, consistency with independent
results from a chemical tracer release experiment is found to provide
additional support to the results.
