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Related papers: Stochastic PDE limit of the dynamic ASEP

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We study the symmetric facilitated exclusion process (FEP) on the finite one-dimensional lattice $\lbrace 1,\dots ,N-1\rbrace$ when put in contact with boundary reservoirs, whose action is subject to an additional kinetic constraint in…

Probability · Mathematics 2026-02-09 Hugo Da Cunha , Clément Erignoux , Marielle Simon

We consider the (discrete) parabolic Anderson model $\partial u(t,x)/\partial t=\Delta u(t,x) +\xi_t(x) u(t,x)$, $t\geq 0$, $x\in \mathbb{Z}^d$, where the $\xi$-field is $\mathbb{R}$-valued and plays the role of a dynamic random…

Probability · Mathematics 2021-03-26 Dirk Erhard , Martin Hairer

Properties of the one-dimensional totally asymmetric simple exclusion process (TASEP), and their connection with the dynamical scaling of moving interfaces described by a Kardar-Parisi-Zhang (KPZ) equation are investigated. With periodic…

Statistical Mechanics · Physics 2008-09-04 S. L. A. de Queiroz , R. B. Stinchcombe

We study the steady state of the two-species Asymmetric Simple Exclusion Process (ASEP) with open boundary conditions. The matrix product method works for the determination of the stationary probability distribution. Several physical…

Statistical Mechanics · Physics 2007-05-23 Masaru Uchiyama

Generalization of the one-dimensional totally asymmetric exclusion process (TASEP) with open boundary conditions in which particles are allowed to jump $l$ sites ahead with the probability $p_l\sim 1/l^{\sigma+1}$ is studied by Monte Carlo…

Statistical Mechanics · Physics 2007-05-23 J. Szavits-Nossan , K. Uzelac

Understanding the behavior of stochastic gradient methods is a central problem in modern machine learning. Recent work has highlighted diagonal linear networks as a simplified yet expressive setting for analyzing the optimization and…

Optimization and Control · Mathematics 2026-05-19 Begoña García Malaxechebarría , Courtney Paquette , Maryam Fazel , Dmitriy Drusvyatskiy

We introduce a new interacting particle system on $\mathbb{Z}$, \emph{slowed $t$-TASEP}. It may be viewed as a $q$-TASEP with additional position-dependent slowing of jump rates depending on a parameter $t$, which leads to discrete and…

Probability · Mathematics 2022-11-08 Roger Van Peski

The asymmetric simple exclusion process (ASEP) plays the role of a paradigm in non-equilibrium statistical mechanics. We review exact results for the ASEP obtained by Bethe ansatz and put emphasis on the algebraic properties of this model.…

Statistical Mechanics · Physics 2009-11-11 O. Golinelli , K. Mallick

We study an interacting particle system in $\mathbf{R}^d$ motivated by Stein variational gradient descent [Q. Liu and D. Wang, NIPS 2016], a deterministic algorithm for sampling from a given probability density with unknown normalization.…

Analysis of PDEs · Mathematics 2018-11-07 Jianfeng Lu , Yulong Lu , James Nolen

We review recent progress in limit laws for the one-dimensional asymmetric simple exclusion process (ASEP) on the integer lattice. The limit laws are expressed in terms of a certain Painlev\'e II function. Furthermore, we take this…

Probability · Mathematics 2011-04-01 Craig A. Tracy , Harold Widom

A new asymptotic expansion scheme for backward SDEs (BSDEs) is proposed.The perturbation parameter is introduced just to scale the forward stochastic variables within a BSDE. In contrast to the standard small-diffusion asymptotic expansion…

Computational Finance · Quantitative Finance 2014-12-23 Masaaki Fujii

The facilitated simple exclusion process (FEP) is a one-dimensional exclusion process with a dynamical constraint. We establish bounds on the mixing time of the FEP on the segment, with closed boundaries, and the circle. The FEP on these…

Probability · Mathematics 2024-03-01 James Ayre , Paul Chleboun

The asymptotic error distribution of numerical methods applied to stochastic ordinary differential equations has been well studied, which characterizes the evolution pattern of the error distribution in the small step-size regime. It is…

Numerical Analysis · Mathematics 2024-11-19 Jialin Hong , Diancong Jin , Xu Wang , Guanlin Yang

We propose an extension of the totally asymmetric simple exclusion process (TASEP) in which particles hopping along a lattice can be blocked by obstacles that dynamically attach/detach from lattice sites. The model can be thought as TASEP…

Statistical Mechanics · Physics 2019-02-20 Bartlomiej Waclaw , Justyna Cholewa-Waclaw , Philip Greulich

We consider the facilitated exclusion process, an interacting particle system on the integer line where particles hop to one of their left or right neighbouring site only when the other neighbouring site is occupied by a particle. A…

Probability · Mathematics 2025-02-04 Guillaume Barraquand , Oriane Blondel , Marielle Simon

The asymmetric simple exclusion exclusion process (ASEP) is a model of particles hopping on a one-dimensional lattice of n sites. It was introduced around 1970, and since then has been extensively studied by researchers in statistical…

Combinatorics · Mathematics 2020-01-15 Sylvie Corteel , Olya Mandelshtam , Lauren Williams

We consider the asymmetric simple exclusion process (ASEP) on a semi-infinite chain which is coupled at the end to a reservoir with a particle density that changes periodically in time. It is shown that the density profile assumes a…

Statistical Mechanics · Physics 2009-11-13 Vladislav Popkov , Mario Salerno , Gunter M. Schutz

We consider the asymmetric exclusion process (ASEP) in one dimension on sites $i = 1,..., N$, in contact at sites $i=1$ and $i=N$ with infinite particle reservoirs at densities $\rho_a$ and $\rho_b$. As $\rho_a$ and $\rho_b$ are varied, the…

Statistical Mechanics · Physics 2007-05-23 B. Derrida , J. L. Lebowitz , E. R. Speer

We study a new process, which we call ASEP$(q,j)$, where particles move asymmetrically on a one-dimensional integer lattice with a bias determined by $q\in (0,1)$ and where at most $2j\in\mathbb{N}$ particles per site are allowed. The…

Probability · Mathematics 2014-07-15 Gioia Carinci , Cristian Giardina' , Frank Redig , Tomohiro Sasamoto

In this paper it is shown that the steady-state weights of the asymmetric simple exclusion process (ASEP) with open boundaries and parallel update can be written as a product of a scalar pair-factorized and a matrix-product state. This type…

Statistical Mechanics · Physics 2015-05-13 Marko Woelki , Michael Schreckenberg