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One reason for the well known fact that the Complex Langevin (CL) method sometimes fails to converge or converges to the wrong limit has been identified long ago: it is insufficient decay of the probability density either near infinity or near poles of the drift, leading to boundary terms that spoil the formal argument for correctness.
O. Philipsen and J. Scheunert, (2019), arXiv:1908.03136 [hep-lat]
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