Localised distributions in complex Langevin dynamics

Complex Langevin dynamics can be used to perform numerical simulations of theories with a complex action. In order to justify the procedure, it is important to understand the properties of the real and positive distribution, which is effectively sampled during the stochastic process. In the context of a simple model, we study this distribution and relate the results to the recently derived criteria for correctness. We demonstrate analytically that if the distribution has support only on a strip in the complexified configuration space, correct results are expected.