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We study the joint exit probabilities of particles in the totally asymmetric simple exclusion process (TASEP) from space-time sets of given form. We extend previous results on the space-time correlation functions of the TASEP, which…

Statistical Mechanics · Physics 2012-08-27 S. S. Poghosyan , A. M. Povolotsky , V. B. Priezzhev

In the asymmetric simple exclusion process on the integers each particle waits exponential time, then with probability p it moves one step to the right if the site is unoccupied, otherwise it stays put; and with probability q=1-p it moves…

Probability · Mathematics 2013-02-18 Craig A. Tracy , Harold Widom

We study the transition probabilities for the totally asymmetric simple exclusion process (TASEP) on the infinite integer lattice with a finite, but arbitrary number of first and second class particles. Using the Bethe ansatz we present an…

Statistical Mechanics · Physics 2010-08-17 Sakuntala Chatterjee , Gunter M. Schütz

In the multi-type totally asymmetric simple exclusion process (TASEP) on the line, each site of Z is occupied by a particle labeled with some number, and two neighboring particles are interchanged at rate one if their labels are in…

Probability · Mathematics 2012-11-16 Gideon Amir , Omer Angel , Benedek Valkó

In this paper we obtain general integral formulas for probabilities in the asymmetric simple exclusion process (ASEP) on the integer lattice with nearest neighbor hopping rates p to the right and q=1-p to the left. For the most part we…

Probability · Mathematics 2011-08-12 Craig A. Tracy , Harold Widom

We introduce new integrable exclusion and zero-range processes on the one-dimensional lattice that generalize the $q$-Hahn TASEP and the $q$-Hahn Boson (zero-range) process introduced in [Pov13] and further studied in [Cor14], by allowing…

Probability · Mathematics 2017-07-10 Guillaume Barraquand , Ivan Corwin

In this paper we study the probability distribution of the position of a tagged particle in the $q$-deformed Totally Asymmetric Zero Range Process ($q$-TAZRP) with site dependent jumping rates. For a finite particle system, it is derived…

Probability · Mathematics 2017-03-28 Eunghyun Lee , Dong Wang

We consider from a microscopic perspective large deviation properties of several stochastic interacting particle systems, using their mapping to integrable quantum spin systems. A brief review of recent work is given and several new results…

Statistical Mechanics · Physics 2015-10-19 Gunter M. Schütz

In earlier work (arXiv:1707.04927) the authors obtained formulas for the probability in the asymmetric simple exclusion process that at time $t$ a particle is at site $x$ and is the beginning of a block of $L$ consecutive particles. Here we…

Mathematical Physics · Physics 2018-07-04 Craig A. Tracy , Harold Widom

We consider the totally asymmetric simple exclusion process (TASEP) starting with a shock discontinuity at the origin, with asymptotic densities $\lambda$ to the left of the origin and $\rho$ to the right of it and $\lambda<\rho$. We find…

Probability · Mathematics 2024-01-24 Patrik L. Ferrari , Peter Nejjar

In this paper, we consider the two-species asymmetric simple exclusion process consisting of $N-1$ first-class particles and one second-class particle. We assume that the second-class particle is the rightmost particle at t=0. We provide an…

Probability · Mathematics 2023-04-05 Eunghyun Lee , Zhanibek Tokebayev

We consider the totally asymmetric simple exclusion process (TASEP) with non-random initial condition having density $\rho$ on $\mathbb{Z}_-$ and $\lambda$ on $\mathbb{Z}_+$, and a second class particle initially at the origin. For…

Probability · Mathematics 2018-05-23 Patrik L. Ferrari , Peter Nejjar , Promit Ghosal

The purpose of this article is to describe the two approaches to compute exact formulas (which are amenable to asymptotic analysis) for the probability distribution of the current of particles past a given site in the asymmetric simple…

Probability · Mathematics 2013-03-13 Ivan Corwin

The Airy process A(t), introduced by Pr\"ahofer and Spohn, is the limiting stationary process for a polynuclear growth model. Adler and van Moerbeke found a PDE in the variables s_1, s_2, and t for the probability that A(0)<s_1 and…

Probability · Mathematics 2009-11-10 Harold Widom

We consider the asymmetric simple exclusion process (ASEP) on the positive integers with an open boundary condition. We show that, when starting devoid of particles and for a certain boundary condition, the height function at the origin…

Probability · Mathematics 2020-01-10 Guillaume Barraquand , Alexei Borodin , Ivan Corwin , Michael Wheeler

For the asymmetric simple exclusion process on the integer lattice with two-sided Bernoulli initial condition, we derive exact formulas for the following quantities: (1) the probability that site x is occupied at time t; (2) a correlation…

Probability · Mathematics 2010-07-26 Craig A. Tracy , Harold Widom

We consider any fixed $d\in\mathbb{Z}_{>0}$ number of second class particles in the asymmetric simple exclusion process (ASEP), constructed via a basic coupling of two ASEPs. We give the joint distribution of the positions of the second…

Probability · Mathematics 2026-04-21 Daniel Adams , Márton Balázs , Jessica Jay

In this paper we treat the multiparticle hopping asymmetric diffusion model (MADM) of which initial configuration is such that a single site is occupied by infinitely many particles and all other sites are empty. We show that the…

Probability · Mathematics 2017-08-16 Eunghyun Lee

The totally asymmetric simple exclusion process (TASEP) on the one-dimensional lattice with the Bernoulli \rho measure as initial conditions, 0<\rho<1, is stationary in space and time. Let N_t(j) be the number of particles which have…

Mathematical Physics · Physics 2013-02-07 Patrik L. Ferrari , Herbert Spohn

An explicit Fredholm determinant formula is derived for the multipoint distribution of the height function of the totally asymmetric simple exclusion process (TASEP) with arbitrary right-finite initial condition. The method is by solving…

Probability · Mathematics 2021-11-25 Konstantin Matetski , Jeremy Quastel , Daniel Remenik