  The mass domain where massive extrasolar planets and brown dwarfs overlap is
still poorly understood due to the paucity of brown dwarfs orbiting close to
solar-type stars, the so-called brown dwarf desert. In this paper we collect
all of available data about close brown dwarfs around solar type stars and
their host stars from literature and study the demographics of the brown dwarf
desert. The data clearly show a short period and a medium mass gap in the brown
dwarf period-mass distribution diagram ($ 35<m\sin i<55 M_{\rm Jup}$ and
$P<100$ days), representing the "driest land" in the brown dwarf desert.
Observation biases are highly unlikely to cause this gap due to its short
period and medium mass, of which brown dwarfs can be easily detected by
previous RV surveys. Brown dwarfs above and below this gap have significantly
different eccentricity distribution, which not only confirms that this gap is
real, but also implies that they may have different origins. Our further
statistical study indicates that brown dwarfs below this gap may primarily form
in the protoplanetary disk through disk gravitational instability, while brown
dwarfs above this gap may dominantly form like a stellar binary through
molecular cloud fragmentation. Our discoveries have offered important insights
about brown dwarf formation mechanisms and their possible relationships with
planet and star formation.
