Related papers: Random Matrices and the Glasgow Method
Partition function zeros steer the critical behavior of a system. Studying four-flavor lattice QCD at finite temperature and density with the Wilson-clover fermion action and the Iwasaki gauge action using a phase-quenched fermion…
It has been suggested that the density of states approach to performing lattice simulations in QCD with nonzero chemical potential can be modified to improve the signal to noise ratio by performing a cumulant expansion of the complex phase…
The gradient discretisation method (GDM) -- a generic framework encompassing many numerical methods -- is studied for a general stochastic Stefan problem with multiplicative noise. The convergence of the numerical solutions is proved by…
Using the language of non-relativistic effective Lagrangians, we formulate a systematic framework for the calculation of resonance matrix elements in lattice QCD. The generalization of the L\"uscher-Lellouch formula for these matrix…
Large-momentum effective theory (LaMET) provides an approach to directly calculate the $x$-dependence of generalized parton distributions (GPDs) on a Euclidean lattice through power expansion and a perturbative matching. When a parton's…
We review the ideas of how random matrix theory has to be properly applied to quantum physics; particularly we focus on how the spectrum has to be properly prepared and the random matrix correctly identified before the random matrix and the…
Random matrices tend to be well conditioned, and we employ this well known property to advance matrix computations. We prove that our algorithms employing Gaussian random matrices are efficient, but in our tests the algorithms have…
Random Matrix Theory (RMT) is a powerful statistical tool to model spectral fluctuations. This approach has also found fruitful application in Quantum Chromodynamics (QCD). Importantly, RMT provides very efficient means to separate…
For a long time, people have been focusing on how to extract more information, such as off-diagonal observables, from the quantum Monte Carlo (QMC) simulation of the partition function, but there have been numerous difficulties, and many of…
Quasi-Monte Carlo (QMC) integration of output functionals of solutions of the diffusion problem with a log-normal random coefficient is considered. The random coefficient is assumed to be given by an exponential of a Gaussian random field…
The statistics of work performed on a system by a sudden random quench is investigated. Considering systems with finite dimensional Hilbert spaces we model a sudden random quench by randomly choosing elements from a Gaussian unitary…
Developments in QCD at finite density are reviewed. I begin by discussing some new algorithms which have been applied to other theories with sign problems. Then I discuss the method of analytic continuation in QCD using a series expansion…
For QCD at non-zero chemical potential $\mu$, the Dirac eigenvalues are scattered in the complex plane. We define a notion of ordering for individual eigenvalues in this case and derive the distributions of individual eigenvalues from…
A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…
A new method based on the concept of probability distribution is proposed to analyze the finite volume energy spectrum in lattice QCD. Using synthetic lattice data, we demonstrate that for the channel with quantum numbers of the…
Recent work found that an analysis formalism based on the Lanczos algorithm allows energy levels to be extracted from Euclidean correlation functions with faster ground-state convergence than effective masses, convergent estimators for…
Lattice quantum chromodynamics (QCD) will soon become the primary theoretical tool in rigorous studies of single- and multi-hadron sectors of QCD. It is truly ab initio meaning that its only parameters are those of standard model. The…
We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence…
We explain how masses and matrix elements can be computed in lattice QCD using Schr"odinger functional boundary conditions. Numerical results in the quenched approximation demonstrate that good precision can be achieved. For a statistical…
We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows…