Related papers: Monte Carlo Simulations with Indefinite and Comple…
We review recent attempts at dealing with the sign problem in Monte Carlo calculations by deforming the region of integration in the path integral from real to complex fields. We discuss the theoretical foundations, the algorithmic issues…
Monte Carlo computer simulations are virtually the only way to analyze the thermodynamic behavior of a system in a precise way. However, the various existing methods exhibit extreme differences in their efficiency, depending on model…
The primary focus of Monte Carlo simulation is to identify and quantify risk related to uncertainty and variability in spreadsheet model inputs. The stress of Monte Carlo simulation often reveals logical errors in the underlying spreadsheet…
We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. This setting is ubiquitous…
We introduce an exact Monte Carlo approach to the statistics of discrete quantum systems which does not rely on the standard fragmentation of the imaginary time, or any small parameter. The method deals with discrete objects, kinks,…
As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the cut sets. In this paper we demonstrate how Multilevel Monte Carlo (MLMC) - a…
Frustrated spin systems generically suffer from the negative sign problem inherent to Monte Carlo methods. Since the severity of this problem is formulation dependent, optimization strategies can be put forward. We introduce a phase pinning…
Monte Carlo simulations of diffusion processes often introduce bias in the final result, due to time discretization. Using an auxiliary Poisson process, it is possible to run simulations which are unbiased. In this article, we propose such…
In this talk we show how the sign problem, occurring in dynamical simulations of random matrices at nonzero chemical potential, can be avoided by judiciously combining matrices into subsets. One can prove that these subsets have real and…
Based on the scaling relation for the dynamics at the early time, a new method is proposed to measure both the static and dynamic critical exponents. The method is applied to the two dimensional Ising model. The results are in good…
We present a new quantum Monte Carlo algorithm suitable for generically complex problems, such as systems coupled to external magnetic fields or anyons in two spatial dimensions. We find that the choice of gauge plays a nontrivial role, and…
We consider the numerical analysis of the inchworm Monte Carlo method, which is proposed recently to tackle the numerical sign problem for open quantum systems. We focus on the growth of the numerical error with respect to the simulation…
Sign problem in quantum Monte Carlo (QMC) simulation appears to be an extremely hard yet interesting problem. In this article, we present a pedagogical overview on the origin of the sign problem in various quantum Monte Carlo simulation…
The sign problem is a notorious problem, which occurs in Monte Carlo simulations of a system with the partition function whose integrand is not real positive. The basic idea of the factorization method applied on such a system is to control…
The combination of continuum Many-Body Quantum physics and Monte Carlo methods provide a powerful and well established approach to first principles calculations for large systems. Replacing the exact solution of the problem with a…
Quantum Monte Carlo is one of the most powerful numerical tools for studying nonpeturbative properties of quantum many-body systems. However, its application to real-time problems is limited since the complex and highly-oscillating…
The nuclear shell model is known to describe the properties of various nuclei extremely well. However, the auxiliary-field quantum Monte Carlo calculations cannot be applied to it with general interactions due to the sign problem. The model…
We explain in detail how to estimate mean values and assess statistical errors for arbitrary functions of elementary observables in Monte Carlo simulations. The method is to estimate and sum the relevant autocorrelation functions, which is…
Techniques for simulating molecules whose conformations satisfy constraints are presented. A method for selecting appropriate moves in Monte Carlo simulations is given. The resulting moves not only obey the constraints but also maintain…
Distortion risk measures play a critical role in quantifying risks associated with uncertain outcomes. Accurately estimating these risk measures in the context of computationally expensive simulation models that lack analytical tractability…