Sign problems, noise, and chiral symmetry breaking in a QCD-like theory
  The Nambu-Jona-Lasinio model reduced to 2+1 dimensions has two different path integral formulations: at finite chemical potential one formulation has a severe sign problem similar to that found in QCD, while the other does not. At large N, where N is the number of flavors, one can compute the probability distributions of fermion correlators analytically in both formulations. In the former case one finds a broad distribution with small mean; in the latter one finds a heavy tailed positive distribution amenable to the cumulant expansion techniques developed in earlier work. We speculate on the implications of this model for QCD. 
Dorota Grabowska, David B. Kaplan and Amy N. Nicholson
hep-lat hep-ph nucl-th