  We obtain the exact ground state for the Calogero-Sutherland problem in
arbitrary dimensions. In the special case of two dimensions, we show that the
problem is connected to the random matrix problem for complex matrices,
provided the strength of the inverse-square interaction $g = 2$. In the
thermodynamic limit, we obtain the ground state energy and the pair-correlation
function and show that in this case there is no long-range order.
