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Monte Carlo simulations of systems with a complex action are known to beextremely difficult. A new approach to this problem based on a factorizationproperty of distribution functions of observables has been proposed recently.The method can be applied to any system with a complex action, and iteliminates the so-called overlap problem completely. We test the new approachin a Random Matrix Theory for finite density QCD, where we are able toreproduce the exact results for the quark number density. The achieved systemsize is large enough to extract the thermodynamic limit. Our results provide aclear understanding of how the expected first order phase transition is inducedby the imaginary part of the action.Comment: 27 pages, 25 figure

The factorization method for systems with a complex action. A test in Random Matrix Theory for finite density QCD