Abstract
It is an old idea to replace averages of observables with respect to a complex weight by expectation values with respect to a genuine probability measure on complexified space. This is precisely what one would like to get from complex Langevin simulations. Unfortunately, these fail in many cases of physical interest. We will describe method of deriving positive representations by matching of moments and show simple examples of successful constructions. It will be seen that the problem is greatly underdetermined.
Highlights
Numerical simulations involving Monte Carlo methods are only possible if averages with respect to genuine probability distributions are to be computed
In [1, 2] it was proposed that probability distribution could be constructed by setting up a stochastic process on complexification of the integration manifold - the idea known as the complex Langevin approach
It is based on directly solving the matching conditions, which express compatibility of probabilistic measure with given complex weight
Summary
Subsection 2.4 contains a brief discussion of distributions on compact group manifolds.
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