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Deriving the time evolution of a distribution of probability (or aprobability density matrix) is a problem encountered frequently in a variety ofsituations: for physical time, it could be a kinetic reaction study, whileidentifying time with the number of computational steps gives a typical pictureof algorithms routinely used in quantum impurity solvers, density functionaltheory, etc. Using a truncation scheme for the expansion of the exact quantityis necessary due to constraints of the numerical implementation. However, thisleads in turn to serious complications such as the Fermion Sign Problem(essentially, density or weights will become negative). By integrating angulardegrees of freedom and reducing the dynamics to the radial component, the timeevolution is reformulated as a nonlinear integral transform of the distributionfunction. A canonical decomposition into orthogonal polynomials leads back tothe original sign problem, but using a characteristic-function representationallows to extract the asymptotic behavior, and gives an exact large-time limit,for many initial conditions, with guaranteed positivity.

Universal limits of nonlinear measure redistribution processes and their applications