It is an old idea to replace averages of observables with respect to complex weight by an average of its analytic continuation to complexified space with respect to some probabilistic measure. This is precisely what one would like to get from complex Langevin simulations. Unfortunately, these fail in many cases of physical interest. In my talk I will describe method of deriving positive representations by matching of moments. I will show simple examples of successful constructions and argue that problem is greatly underdetermined.

Theoretical Developments