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Related papers: Asymptotics in ASEP with Step Initial Condition

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We study the one-dimensional asymmetric simple exclusion process (ASEP) with open boundary conditions. Particles are injected and ejected at both boundaries. It is clarified that the steady state of the model is intimately related to the…

Statistical Mechanics · Physics 2009-11-10 Masaru Uchiyama , Tomohiro Sasamoto , Miki Wadati

We study the facilitated totally asymmetric exclusion process on the one dimensional integer lattice. We investigate the invariant measures and the limiting behavior of the process. We mainly derive the limiting distribution of the process…

Probability · Mathematics 2018-09-03 Dayue Chen , Linjie Zhao

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

We prove duality relations for two interacting particle systems: the $q$-deformed totally asymmetric simple exclusion process ($q$-TASEP) and the asymmetric simple exclusion process (ASEP). Expectations of the duality functionals correspond…

Probability · Mathematics 2014-10-28 Alexei Borodin , Ivan Corwin , Tomohiro Sasamoto

A discrete-time totally asymmetric simple exclusion process on a lattice with open boundaries is considered. There are particles of different types. The type of a particle is characterized by the probability that a particle moves to a…

Statistical Mechanics · Physics 2025-11-04 Marina V. Yashina , Alexander G. Tatashev

We study two versions of the asymmetric exclusion process (ASEP) -- an ASEP on a semi-infinite lattice with an open left boundary, and an ASEP on a finite lattice with open left and right boundaries -- and we demonstrate a surprising…

Statistical Mechanics · Physics 2012-04-06 Tomohiro Sasamoto , Lauren Williams

Many integrable stochastic particle systems in one space dimension (such as TASEP - totally asymmetric simple exclusion process - and its various deformations, with a notable exception of ASEP) remain integrable when we equip each particle…

Probability · Mathematics 2021-03-09 Leonid Petrov

We investigate the asymmetric simple exclusion process (ASEP) on an interval with open boundaries. We provide a representation for its stationary distribution as a marginal of the top layer of a two-layer ensemble under Liggett's condition.…

Probability · Mathematics 2025-02-10 Wlodek Bryc

In this paper we consider the totally asymmetric simple exclusion process, with non-random initial condition having three regions of constant densities of particles. From left to right, the densities of the three regions are increasing.…

Mathematical Physics · Physics 2020-01-08 Patrik L. Ferrari , Peter Nejjar

The asymmetric simple exclusion process (ASEP) is a paradigmatic nonequilibrium many-body system that describes the asymmetric random walk of particles with exclusion interactions in a lattice. Although the ASEP is recognized as an exactly…

Statistical Mechanics · Physics 2024-03-05 Yuki Ishiguro , Jun Sato

We study the distribution of the smallest eigenvalue for certain classes of positive-definite Hermitian random matrices, in the limit where the size of the matrices becomes large. Their limit distributions can be expressed as Fredholm…

Mathematical Physics · Physics 2016-12-07 Tom Claeys , Manuela Girotti , Dries Stivigny

In this paper we consider the TASEP with second class particles with the initial order is such that $k$ first class particles are located to the left of $N-k$ second class particles. Under this assumption of the initial state of order, we…

Probability · Mathematics 2018-01-17 Eunghyun Lee

We consider a finite one-dimensional totally asymmetric simple exclusion process (TASEP) with four types of particles, $\{1,0,\bar{1},*\}$, in contact with reservoirs. Particles of species $0$ can neither enter nor exit the lattice, and…

Statistical Mechanics · Physics 2019-11-11 Erik Aas , Arvind Ayyer , Svante Linusson , Samu Potka

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 study the totally asymmetric simple exclusion process (TASEP) on $\mathbb{Z}$ with step initial condition, in which all particles have distinct types. Our main object of interest is the type of the rightmost particle -- the leader -- at…

Probability · Mathematics 2026-01-30 Alexei Borodin , Alexey Bufetov

We consider the totally asymmetric simple exclusion process with \emph{soft-shock} initial particle density, which is a step function increasing in the direction of flow and the step size chosen small to admit KPZ scaling. The initial…

Probability · Mathematics 2020-10-16 Jeremy Quastel , Mustazee Rahman

As the simplest model of transport of interacting particles in a disordered medium, we consider the asymmetric simple exclusion process (ASEP) in which particles with hard-core interactions perform biased random walks, on the supercritical…

Statistical Mechanics · Physics 2024-12-16 Chandrashekar Iyer , Mustansir Barma , Hunnervir Singh , Deepak Dhar

Introduced in the late 1960's, the asymmetric exclusion process (ASEP) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a one-dimensional lattice of n sites with…

Combinatorics · Mathematics 2022-04-27 Sylvie Corteel , Lauren Williams

The asymptotic behavior of the tail probabilities for the first hitting times of the Bessel process with arbitrary index is shown without using the explicit expressions for the distribution function obtained in the authors' previous works.

Probability · Mathematics 2016-02-17 Yuji Hamana , Hiroyuki Matsumoto

We consider the totally asymmetric simple exclusion process (TASEP) in discrete time with the sublattice parallel dynamics describing particles moving to the right on the one-dimensional infinite chain with equal hoping probabilities. Using…

Statistical Mechanics · Physics 2010-07-19 S. S. Poghosyan , V. B. Priezzhev , G. M. Schütz