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In recent years, there has been remarkable progress in theoreticaljustification of the complex Langevin method, which is a promising method forevading the sign problem in the path integral with a complex weight. Therestill remains, however, an issue concerning occasional failure of this methodin the case where the action involves logarithmic singularities such as the oneappearing from the fermion determinant in finite density QCD. In this talk, wepoint out that this failure is due to the breakdown of the relation between thecomplex weight which satisfies the Fokker-Planck equation and the probabilitydistribution generated by the stochastic process. In fact, this kind of failurecan occur in general when the stochastic process involves a singular driftterm. We show, however, in simple examples, that there exists a parameterregion in which the method works although the standard reweighting method ishardly applicable.

Understanding the problem with logarithmic singularities in the complex Langevin method