相关论文: Complex Langevin and boundary terms

We provide quantitative bounds on the convergence to stationarity of real-valued Langevin diffusions with symmetric target densities.

Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…

We study the numerical approximation of time-dependent, possibly degenerate, second-order Hamilton-Jacobi-Bellman equations in bounded domains with nonhomogeneous Dirichlet boundary conditions. It is well known that convergence towards the…

Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…

QCD at nonzero baryon chemical potential suffers from the sign problem, due to the complex quark determinant. Complex Langevin dynamics can provide a solution, provided certain conditions are met. One of these conditions, holomorphicity of…

In this note, we consider the construction of a one-dimensional stable Langevin type process confined in the upper half-plane and submitted to reflective-diffusive boundary conditions whenever the particle position hits 0. We show that two…

Many important physical problems, such as fluid structure interaction or conjugate heat transfer, require numerical methods that compute boundary derivatives or fluxes to high accuracy. This paper proposes a novel alternative to calculating…

In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…

We explore conditions for when the gradient of a deep declarative node can be approximated by ignoring constraint terms and still result in a descent direction for the global loss function. This has important practical application when…

We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…

In this article we develop a high order accurate method to solve the incompressible boundary layer equations in a provably stable manner.~We first derive continuous energy estimates,~and then proceed to the discrete setting.~We formulate…

A brief overview of the QCD phase diagram at nonzero temperature and density is provided. It is explained why standard lattice QCD techniques are not immediately applicable for its determination, due to the sign problem. We then discuss a…

We present two methods for proving confluence of left-linear term rewrite systems. One is hot-decreasingness, combining the parallel/development closedness theorems with rule labelling based on a terminating subsystem. The other is…

The introduction of a lattice converts a singular boundary-layer problem in the continuum into a regular perturbation problem. However, the continuum limit of the discrete problem is extremely nontrivial and is not completely understood.…

QCD at non-zero chemical potential ($\mu$) for quark number has a complex fermion determinant and thus standard simulation methods for lattice QCD cannot be applied. We therefore simulate this theory using the Complex-Langevin algorithm…

In this note, we establish a new exact worst-case linear convergence rate of the proximal gradient method in terms of the proximal gradient norm, which complements the recent results in [1] and implies a refined descent lemma.descent lemma.…

In this article, we study the pointwise asymptotic behavior of iterated convolutions on the one dimensional lattice Z. We generalize the so-called local limit theorem in probability theory to complex valued sequences. A sharp rate of…

We examine the applicability of diffusive lattice Boltzmann methods to simulate the fluid transport through barrier coatings, finding excellent agreement between simulations and analytical predictions for standard parameter choices. To…

We examine the last-iterate convergence rate of Bregman proximal methods - from mirror descent to mirror-prox and its optimistic variants - as a function of the local geometry induced by the prox-mapping defining the method. For generality,…

Large language models perform reliably when their outputs can be checked: solving equations, writing code, retrieving facts. They perform differently when checking is impossible, as when a clinician chooses an irreversible treatment on…