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Related papers: TASEP fluctuations with soft-shock initial data

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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

We consider the TASEP on Z with two blocks of particles having different jump rates. We study the large time behavior of particles' positions. It depends both on the jump rates and the region we focus on, and we determine the complete…

Mathematical Physics · Physics 2010-03-03 Alexei Borodin , Patrik L. Ferrari , Tomohiro Sasamoto

We prove a strong law of large numbers for the location of the second class particle in a totally asymmetric exclusion process when the process is started initially from a decreasing shock. This completes a study initiated in Ferrari and…

Probability · Mathematics 2007-05-23 Thomas Mountford , Herve Guiol

We study the fluctuation properties of the asymmetric simple exclusion process (ASEP) on an infinite one-dimensional lattice. When $N$ particles are initially situated in the negative region with a uniform density $\rho_-=1$, Johansson…

Statistical Mechanics · Physics 2009-11-10 Taro Nagao , Tomohiro Sasamoto

We consider the totally asymmetric simple exclusion process with initial conditions generating a shock. The fluctuations of particle positions are asymptotically governed by the randomness around the two characteristic lines joining at the…

Mathematical Physics · Physics 2018-04-18 P. L. Ferrari

Current fluctuations for the one-dimensional totally asymmetric exclusion process (TASEP) connected to reservoirs of particles, and their large scale limit to the KPZ fixed point in finite volume, are studied using exact methods. Focusing…

Statistical Mechanics · Physics 2024-10-22 Sylvain Prolhac

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

The one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property of a tagged particle in TASEP with the step-type initial condition. Calculated is the multi-time joint distribution…

Mathematical Physics · Physics 2007-08-18 T. Imamura , T. Sasamoto

We consider the totally asymmetric simple exclusion process in a critical scaling parametrized by $a\geq0$, which creates a shock in the particle density of order $aT^{-1/3},$ $T$ the observation time. When starting from step initial data,…

Probability · Mathematics 2018-10-25 Peter Nejjar

We consider the totally asymmetric simple exclusion process, a model in the KPZ universality class. We focus on the fluctuations of particle positions starting with certain deterministic initial conditions. For large time t, one has regions…

Mathematical Physics · Physics 2008-11-01 Alexei Borodin , Patrik L. Ferrari , Tomohiro Sasamoto

The dynamics of an asymmetric tracer in the symmetric simple exclusion process (SEP) is mapped, in the continuous scaling limit, to the local current through the origin in the zero-range process (ZRP) with a biased bond. This allows us to…

Statistical Mechanics · Physics 2022-11-23 Rahul Dandekar , Kirone Mallick

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

We consider the asymmetric simple exclusion process on $\mathbb{Z}$ with a single second class particle initially at the origin. The first class particles form two rarefaction fans which come together at the origin, where the large time…

Probability · Mathematics 2020-06-24 Peter Nejjar

The one-dimensional totally asymmetric simple exclusion process (TASEP), a Markov process describing classical hard-core particles hopping in the same direction, is considered on a periodic lattice of $L$ sites. The relaxation to the…

Statistical Mechanics · Physics 2016-03-09 Sylvain Prolhac

We study the Facilitated TASEP, an interacting particle system on the one dimensional integer lattice. We prove that starting from step initial condition, the position of the rightmost particle has Tracy Widom GSE statistics on a cube root…

Probability · Mathematics 2024-12-13 Jinho Baik , Guillaume Barraquand , Ivan Corwin , Toufic Suidan

We study the effect of a single driven tracer particle in a bath of other particles performing the random average process on an infinite line using a stochastic hydrodynamics approach. We consider arbitrary fixed as well as random initial…

Statistical Mechanics · Physics 2016-11-03 A. Kundu , J. Cividini

We consider the q-Hahn TASEP which is a three-parameter family of discrete time interacting particle systems. The particles jump to the right independently according to a certain q-Binomial distribution with parallel updates. It is a…

Probability · Mathematics 2019-05-20 Bálint Vető

We consider all totally asymmetric simple exclusion processes (TASEPs) whose transition probabilities are given in the Sch\"utz-type formulas and which jump with homogeneous rates. We show that the multi-point distribution of particle…

Probability · Mathematics 2023-01-10 Yuta Arai

The totally asymmetric simple exclusion process (TASEP) on Z with the Bernoulli-rho measure as initial conditions, 0<rho<1, is stationary. It is known that along the characteristic line, the current fluctuates as of order t^{1/3}. The…

Mathematical Physics · Physics 2012-10-29 Jinho Baik , Patrik L. Ferrari , Sandrine Péché

We investigate the asymptotic fluctuation of three interacting particle systems: the geometric q-TASEP, the geometric q-PushTASEP and the q-PushASEP. We prove that the rescaled particle position converges to the GUE Tracy-Widom distribution…

Probability · Mathematics 2022-03-18 Bálint Vető