A subset solution to the sign problem in simulations at non-zero chemical potential

At nonzero quark chemical potential lattice QCD simulations with dynamical quarks are hampered by the sign problem caused by the complex fermion determinant. In this talk we discuss the relation between QCD and random matrix theory and present a novel solution to the sign problem in dynamical random matrix simulations. The sign problem is solved by gathering matrices in subsets, whose sums of complex determinants are real and positive. Markov chains of relevant subsets were generated in Monte Carlo simulations and various observables, like the chiral condensate and quark number, were accurately computed. The subset formula, which is at the basis of the positivity proof for the subset weights, also provides a simple solution to the Silver Blaze puzzle.