  We propose a new method for simulating QCD at finite density, where
interesting phases such as the color superconductivity phase is conjectured to
appear. The method is based on a general factorization property of distribution
functions of observables, and it is therefore applicable to any system with a
complex action. The so-called overlap problem is completely eliminated by the
use of constrained simulations. We test this method in a Random Matrix Theory
for finite density QCD, where we are able to reproduce the exact results for
the quark number density. The achieved system size is large enough to extract
the thermodynamic limit. Our results provide a clear understanding of how the
expected first order phase transition is induced by the imaginary part of the
action. We also discuss the noncommutativity of the zero chemical potential
limit and the thermodynamic limit, which is relevant to recent Monte Carlo
studies at small chemical potential.
