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Related papers: Integral formulas of ASEP and $q$-TAZRP on a ring

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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

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

The asymmetric simple exclusion process (ASEP) is a paradigm for non-equilibrium physics that appears as a building block to model various low-dimensional transport phenomena, ranging from intracellular traffic to quantum dots. We review…

Statistical Mechanics · Physics 2015-05-27 Kirone Mallick

We consider the totally asymmetric exclusion process on a ring in discrete time with the backward-ordered sequential update and particle-dependent hopping probabilities. Using a combinatorial treatment of the Bethe ansatz, we derive the…

Statistical Mechanics · Physics 2008-07-02 V. S. Poghosyan , V. B. Priezzhev

We present explicit formulas for total crossing events in the multi-species asymmetric exclusion process ($r$-ASEP) with underlying $U_q(\widehat{\mathfrak{sl}}_{r+1})$ symmetry. In the case of the two-species TASEP these can be derived…

Mathematical Physics · Physics 2023-06-05 Jan de Gier , William Mead , Michael Wheeler

We study the integrable two-species asymmetric simple exclusion process (ASEP) for two inequivalent types of open, non particle conserving boundary conditions. Employing the nested off-diagonal Bethe ansatz method, we construct for each…

Mathematical Physics · Physics 2019-05-07 Xin Zhang , Fakai Wen , Jan de Gier

We consider the asymmetric simple exclusion process (ASEP) with forward hopping rate 1, backward hopping rate q and periodic boundary conditions. We show that the Bethe equations of ASEP can be decoupled, at all order in perturbation in the…

Statistical Mechanics · Physics 2021-09-08 Sylvain Prolhac

In this paper we consider the $q$-deformed totally asymmetric zero range process ($q$-TAZRP), also known as the $q$-boson (stochastic) particle system, on the ${\mathbb Z}$ lattice, such that the jump rate of a particle depends on the site…

Probability · Mathematics 2016-04-15 Dong Wang , David Waugh

We find the formulas of the transition probabilities of the $N$-particle multi-species asymmetric simple exclusion processes (ASEP), and show that the transition probabilities are written as a determinant when the order of particles in the…

Mathematical Physics · Physics 2020-12-22 Eunghyun Lee

We show that in the asymmetric simple exclusion process (ASEP) on a ring, conditioned on carrying a large flux, the particle experience an effective long-range potential which in the limit of very large flux takes the simple form $U=…

Statistical Mechanics · Physics 2010-07-29 Vladislav Popkov , Gunter M. Schütz , Damien Simon

We consider the totally asymmetric simple exclusion process on a ring with flat and step initial conditions. We assume that the size of the ring and the number of particles tend to infinity proportionally and evaluate the fluctuations of…

Mathematical Physics · Physics 2017-03-02 Jinho Baik , Zhipeng Liu

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

We treat the $N$-particle ZRP whose jumping rates satisfy a certain condition. This condition is required to use the Bethe ansatz and the resulting model is the $q$-boson model that appeared in [J. Phys. A, \textbf{31} 6057--6071 (1998)] by…

Mathematical Physics · Physics 2015-06-17 Marko Korhonen , Eunghyun Lee

We give contour integral formulas for the generating function of the joint distribution of the PushASEP on a ring. We obtained these formulas through a rigorous treatment of Bethe Ansatz. The approach relies on residue computations and…

Probability · Mathematics 2023-08-11 Jhih-Huang Li , Axel Saenz

We write explicit contour integral formulas for probability distributions of the multi-species q-TAZRP and the multi-species ASEP starting with q-exchangeable initial conditions. The formulas are equal to the corresponding explicit contour…

Probability · Mathematics 2019-03-29 Jeffrey Kuan

The one-dimensional asymmetric simple exclusion process (ASEP), where $N$ hard-core particles hop forward with rate $1$ and backward with rate $q<1$, is considered on a periodic lattice of $L$ site. Using KPZ universality and previous…

Statistical Mechanics · Physics 2016-10-19 Sylvain Prolhac

We consider the totally asymmetric simple exclusion process (TASEP) on a periodic one-dimensional lattice of L sites. Using Bethe ansatz, we derive parametric formulas for the eigenvalues of its generator in the thermodynamic limit. This…

Statistical Mechanics · Physics 2013-10-02 Sylvain Prolhac

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

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 consider the asymmetric simple exclusion processes (ASEP) on a ring constrained to produce an atypically large flux, or an extreme activity. Using quantum free fermion techniques we find the time-dependent conditional transition…

Statistical Mechanics · Physics 2015-05-20 V. Popkov , G. M. Schütz
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