Related papers: Scaling properties of multiscale equilibration
We revisit the classical problem of approximating a stochastic differential equation by a discrete-time and discrete-space Markov chain. Our construction iterates Caratheodory's theorem over time to match the moments of the increments…
This chapter discusses the conditions and timescales under which isolated many-body quantum systems, initially far from equilibrium, ultimately reach thermal equilibrium. We also examine quantities that, during the relaxation process,…
In this work I apply a recently proposed improvement procedure, originally conceived to reduce finite lattice spacing effects in transfer matrices for dilute Fermi systems, to tuning operators for the calculation of observables. I…
In the context of Monte Carlo sampling for lattice models, the complexity of the energy landscape often leads to Markov chains being trapped in local optima, thereby increasing the correlation between samples and reducing sampling…
Using experiments on a colloidal particle trapped in an optical tweezer, we confirm a recent proposal to increase the effective mobility or clock rate of systems described by Langevin dynamics, by simultaneously scaling deterministic forces…
Markov chain Monte Carlo algorithms are invaluable tools for exploring stationary properties of physical systems, especially in situations where direct sampling is unfeasible. Common implementations of Monte Carlo algorithms employ…
We develop a practical approach to establish the stability, that is, the recurrence in a given set, of a large class of controlled Markov chains. These processes arise in various areas of applied science and encompass important numerical…
The relative smoothing rates of various gauge field smoothing algorithms are investigated on ${\cal O}(a^2)$-improved $\suthree$ Yang--Mills gauge field configurations. In particular, an ${\cal O}(a^2)$-improved version of APE smearing is…
In theories with topological sectors, such as lattice QCD and four-dimensional SU(N) gauge theories with periodic boundary conditions, conventional update algorithms suffer from topological freezing due to large action barriers separating…
In lattice quantum field theory studies, parameters defining the lattice theory must be tuned toward criticality to access continuum physics. Commonly used Markov chain Monte Carlo (MCMC) methods suffer from critical slowing down in this…
Scaled type Markov renewal processes generalize classical renewal processes: renewal times come from a one parameter family of probability laws and the sequence of the parameters is the trajectory of an ergodic Markov chain. Our primary…
Computing smoothing distributions, the distributions of one or more states conditional on past, present, and future observations is a recurring problem when operating on general hidden Markov models. The aim of this paper is to provide a…
The deconfinement transition is studied close to the continuum limit of SO(3) lattice gauge theory. High barriers for tunnelling among different twist sectors causing loss of ergodicity for local update algorithms are circumvented by means…
In this paper, we investigate the use of a mass lumped fully explicit time stepping scheme for the discretisation of the wave equation with underlying material parameters that vary at arbitrarily fine scales. We combine the leapfrog scheme…
We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to…
Atomistic simulations provide valuable insights into the physical processes governing material behavior. However, their applicability is fundamentally constrained by the limited time scales accessible to brute-force simulations. This…
Simulating physical problems involving multi-time scale coupling is challenging due to the need of solving these multi-time scale processes simultaneously. In response to this challenge, this paper proposed an explicit multi-time step…
Inspired by the Kadanoff transformation in the standard renormalization group theory, we propose a temporal renormalization scheme. A Boltzmann factor that explicitly depends on the renormalized timescale is constructed, permitting…
Recent applications of machine-learned normalizing flows to sampling in lattice field theory suggest that such methods may be able to mitigate critical slowing down and topological freezing. However, these demonstrations have been at the…
Scaling analysis exploiting timescale separation has been one of the most important techniques in the quantitative analysis of nonlinear dynamical systems in mathematical and theoretical biology. In the case of enzyme catalyzed reactions,…