  Due to the presence of light pions in the theory, lattice QCD at finite
densities suffers from issues with noise in both grand canonical and canonical
formulations. We study two different formulations of the Nambu-Jona-Lasinio
model reduced to 2+1 dimensions at large N, where N is the number of flavors.
At finite chemical potential one formulation has a severe sign problem and a
fermion correlator which displays a broad probability distribution with small
mean. In the other we find no sign problem and a distribution amenable to the
cumulant expansion techniques developed in earlier work.
