Related papers: Necessary and sufficient conditions for correctnes…
We discuss recent developments regarding the use of kernels in complex Langevin simulations. In particular, we outline how a kernel can be used to solve the problem of wrong convergence in a simple toy model. Since conventional correctness…
The Complex Langevin (CL) method to simulate `complex probabilities', ideally produces expectation values for the observables that converge to a limit equal to the expectation values obtained with the original complex `probability' measure.…
Complex Langevin simulations are an attempt to solve the sign (or complex-action) problem encountered in various physical systems of interest. The method is based on a complexification of the underlying degrees of freedom and an evolution…
There are problems in physics and particularly in field theory which are defined by complex valued weight functions $e^{-S}$ where $S$ is a polynomial action $S: R^n \rightarrow C $. The conditions under which a convergent complex Langevin…
The complex Langevin approach is a promising method for the numerical treatment of systems with a sign problem, for which conventional lattice field theory techniques based on importance sampling cannot be applied. However, complex Langevin…
The complex Langevin method is a promising approach to the complex-action problem based on a fictitious time evolution of complexified dynamical variables under the influence of a Gaussian noise. Although it is known to have a restricted…
Complex Langevin dynamics can be used to perform numerical simulations of theories with a complex action. In order to justify the procedure, it is important to understand the properties of the real and positive distribution, which is…
In complex Langevin simulations, the insufficient decay of the probability density near infinity leads to boundary terms that spoil the formal argument for correctness. We present a formulation of this term that is cheaply measurable in…
The Complex Langevin (CL) method sometimes shows convergence to the wrong limit, even though the Schwinger-Dyson Equations (SDE) are fulfilled. We analyze this problem in a more general context for the case of one complex variable. We prove…
The method of complex Langevin simulations is a tool that can be used to tackle the complex-action problem encountered, for instance, in finite-density lattice quantum chromodynamics or real-time lattice field theories. The method is based…
A positive representation for a set of complex densities is constructed. In particular, complex measures on a direct product of U(1) groups are studied. After identifying general conditions which such representations should satisfy, several…
We study the identification of direct and indirect causes on time series and provide conditions in the presence of latent variables, which we prove to be necessary and sufficient under some graph constraints. Our theoretical results and…
The complex Langevin method is a leading candidate for solving the sign problem occurring in various physical situations, notably QCD at finite chemical potential. Its most vexing problem is `convergence to the wrong limit', where the…
As is well known the Complex Langevin (CL) method sometimes fails to converge or converges to the wrong limit. We identified one reason for this long ago: insufficient decay of the probability density either near infinity or near poles of…
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…
Under a mild technical assumption, we prove a necessary and sufficient condition for a totally real compacdt set in $\mathbb{C}^n$ to be rationally convex. This generalizes a classical result of Duval-Sibony
The complex Langevin method (CLM) provides a promising way to perform the path integral with a complex action using a stochastic equation for complexified dynamical variables. It is known, however, that the method gives wrong results in…
Complex phenomena in engineering and the sciences are often modeled with computationally intensive feed-forward simulations for which a tractable analytic likelihood does not exist. In these cases, it is sometimes necessary to estimate an…
We derive the necessary and sufficient condition for almost sure convergence of the sequence of measurable functions, and consider some applications in the theory of Fourier series and in the theory of random fields.
The problem of finding a positive distribution, which corresponds to a given complex density, is studied. By the requirement that the moments of the positive distribution and of the complex density are equal, one can reduce the problem to…