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The purpose of this article is to provide an exposition of domains of convergence of power series of several complex variables without recourse to relatively advanced notions of convexity.
We show how contour deformations may be used to control the sign problem of lattice Monte Carlo calculations with non-holomorphic actions. Such actions arise naturally in quantum mechanical scattering problems. The approach is demonstrated…
We propose a framework based on the concept of the semigroup to understand the fermion sign problem. By using properties of contraction semigroups, we obtain sufficient conditions for quantum lattice fermion models to be sign-problem-free.…
Recent progress of the complex Langevin method and the Lefschetz thimble in connection with the sign problem is reviewed. These methods rely on the complexification of the original field manifold and they allow direct simulations of…
In the landscape of approaches toward the simulation of Lattice Models with complex action the Complex Langevin (CL) appears as a straightforward method with a simple, well defined setup. Its applicability, however, is controlled by certain…
The evaluation of the interaction between objects arranged on a lattice requires the computation of lattice sums. A scenario frequently encountered are systems governed by the Helmholtz equation in the context of electromagnetic scattering…
Monte Carlo algorithms are barely considered in spin foam quantum gravity. Due to the quantum nature of spin foam amplitudes one cannot readily apply them, and the present sign problem is a threat to convergence and thus efficiency. Yet,…
Monte Carlo study of the Schwinger model (quantum electrodynamics in one spatial dimension) with a topological $\theta$ term is very difficult due to the sign problem in the conventional lattice formulation. In this paper, we point out that…
Gaussian process is a very promising novel technology that has been applied to both the regression problem and the classification problem. While for the regression problem it yields simple exact solutions, this is not the case for the…
A rigourous Monte Carlo method for protein folding simulation on lattice model is introduced. We show that a parameter which can be seen as the rigidity of the conformations has to be introduced in order to satisfy the detailed balance…
Non-perturbative formulations of field theories are essential to capture intriguing physical phenomena, including confinement in QCD, spontaneous supersymmetry breaking, and dynamical compactification in superstrings. Lattice regularization…
We introduce a mesoscopic three-dimensional Lattice Boltzmann Model which attempts to mimick the physical features associated with cage effects in dynamically heterogeneous fluids. To this purpose, we extend the standard Lattice Boltzmann…
Lattice Green functions appear in lattice gauge theories, in lattice models of statistical physics and in random walks. Here, space coordinates are treated as parameters and series expansions in the mass are obtained. The singular points in…
A possible solution of the notorious sign problem preventing direct Monte Carlo calculations for systems with non-zero chemical potential is to deform the integration region in the complex plane to a Lefschetz thimble. We investigate this…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
We propose a fast and general predecision scheme for Metropolis Monte Carlo simulation of $d$-dimensional long-range interacting lattice models. For potentials of the form $V(r)=r^{-d-\sigma}$, this reduces the computational complexity from…
The first paper in this series introduced a new approach to strong convergence of random matrices that is based primarily on soft arguments. This method was applied to achieve a refined qualitative and quantitative understanding of strong…
We present results of the numerical simulation of the two-dimensional Thirring model at finite density and temperature. The severe sign problem is dealt with by deforming the domain of integration into complex field space. This is the first…
Composite optimization problems, where the sum of a smooth and a merely lower semicontinuous function has to be minimized, are often tackled numerically by means of proximal gradient methods as soon as the lower semicontinuous part of the…
We clarify regions where the canonical approach works well at the finite temperature and density in the Nambu-Jona-Lasinio (NJL) and Polyakov-NJL (PNJL) models. The canonical approach is a useful method for avoiding the sign problem in…