Related papers: Restricted sandpile revisited
This paper introduces a new Markov Chain Monte Carlo method for Bayesian variable selection in high dimensional settings. The algorithm is a Hastings-Metropolis sampler with a proposal mechanism which combines a Metropolis Adjusted Langevin…
Monte Carlo simulations are widely used to simulate complex molecular systems, but standard approaches suffer from metastability. Lately, the use of non-local proposal updates in a collective-variable (CV) space has been proposed in several…
We derive the steady state properties of a general directed ``sandpile'' model in one dimension. Using a central limit theorem for dependent random variables we find the precise conditions for the model to belong to the universality class…
Motivated by the recent contribution \cite{BB17} we study the scaling limit behavior of a class of one-dimensional stochastic differential equations which has a unique attracting point subject to a small additional repulsive perturbation.…
In reason of the strongly non-ergodic dynamical behavior, universality properties of deterministic Fixed-Energy Sandpiles are still an open and debated issue. We investigate the one-dimensional model, whose microscopical dynamics can be…
During the last fourteen years several exact results were obtained for the so-called boundary sine-Gordon model. In the case of a conformal bulk this 2D boundary quantum field theory describes the universal scaling behavior of the…
We perform simulations for long hard-sphere polymer chains using a recently developed binary-tree based Monte Carlo method. Systems in two to five dimensions with free and periodic boundary conditions and up to $10^7$ repeat units are…
We consider the abelian sandpile model and the uniform spanning unicycle on random planar maps. We show that the sandpile density converges to 5/2 as the maps get large. For the spanning unicycle, we show that the length and area of the…
In Monte Carlo calculations of expectation values in lattice quantum field theories, the stochastic variance of the sampling procedure that is used defines the precision of the calculation for a fixed number of samples. If the variance of…
We give an asymptotic formula for the single site height distribution of Abelian sandpiles on $\mathbb{Z}^d$ as $d \to \infty$, in terms of $\mathsf{Poisson}(1)$ probabilities. We provide error estimates.
We consider the Bak-Tang-Wiesenfeld sandpile model on a two-dimensional square lattice of lattice sizes up to L=4096. A detailed analysis of the probability distribution of the size, area, duration and radius of the avalanches will be…
We investigate the sandpile model with Yukawa-type interactions, whose effective range is tuned by an external parameter $R$. Our results reveal that at specific values of $R$, the system exhibits giant avalanches that span the system,…
We construct a driven sandpile slope model and study it by numerical simulations in one dimension. The model is specified by a threshold slope $\sigma_c\/$, a parameter $\alpha\/$, governing the local current-slope relation (beyond…
This survey is an extended version of lectures given at the Cornell Probability Summer School 2013. The fundamental facts about the Abelian sandpile model on a finite graph and its connections to related models are presented. We discuss…
For the task of sampling from a density $\pi \propto \exp(-V)$ on $\mathbb{R}^d$, where $V$ is possibly non-convex but $L$-gradient Lipschitz, we prove that averaged Langevin Monte Carlo outputs a sample with $\varepsilon$-relative Fisher…
In this paper, we study the problem of sampling from a given probability density function that is known to be smooth and strongly log-concave. We analyze several methods of approximate sampling based on discretizations of the (highly…
We study a stochastic lattice gas of particles undergoing asymmetric diffusion in two dimensions. Transitions between a low-density uniform phase and high-density non-uniform phases characterized by localized or extended structure are…
Langevin algorithms are popular Markov chain Monte Carlo methods that are often used to solve high-dimensional large-scale sampling problems in machine learning. The most classical Langevin Monte Carlo algorithm is based on the overdamped…
Transition pathways of stochastic dynamical systems are typically approximated by instantons. Here we show, using a dynamical system containing two competing pathways, that at low-to-intermediate temperatures, instantons can fail to capture…
Quasi-stationary distributions (QSDs)arise from stochastic processes that exhibit transient equilibrium behaviour on the way to absorption QSDs are often mathematically intractable and even drawing samples from them is not straightforward.…