English
Related papers

Related papers: Tracy-Widom asymptotics for q-TASEP

200 papers

In this paper, we consider zero range process with an initial condition which is equivalent to step initial condition in total asymmetric simple exclusion process (TASEP) as described in a paper by R\'akos, A. and Sch\"utz by using…

Mathematical Physics · Physics 2012-09-18 Jen Keng OYoung

Backwards geodesics for TASEP were introduced in [Fer18]. We consider flat initial conditions and show that under proper scaling its end-point converges to maximizer argument of the Airy$_2$ process minus a parabola. We generalize its…

Probability · Mathematics 2024-12-17 Patrik L. Ferrari , Min Liu

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

The totally asymmetric simple exclusion process (TASEP) is a paradigmatic stochastic model for non-equilibrium physics, and has been successfully applied to describe active transport of molecular motors along cytoskeletal filaments.…

Biological Physics · Physics 2018-07-25 Mareike Bojer , Isabella R. Graf , Erwin Frey

In this paper, we obtain the transition probability formulas for the Asymmetric Simple Exclusion Process (ASEP) and the $q$-deformed Totally Asymmetric Zero Range Process ($q$-TAZRP) on the ring by applying the coordinate Bethe ansatz. We…

Probability · Mathematics 2020-10-28 Zhipeng Liu , Axel Saenz , Dong Wang

The decay of a quasiparticle in an isolated quantum dot is considered. At relatively small time the probability to find the system in the initial state decays exponentially: $P(t)\sim \exp(-\Gamma t)$, in accordance with the golden rule.…

Mesoscale and Nanoscale Physics · Physics 2007-05-23 P. G. Silvestrov

Asymptotic Kardar-Parisi-Zhang (KPZ) properties are investigated in the totally asymmetric simple exclusion process (TASEP) with a localized geometric defect. In particular, we focus on the universal nature of nonequilibrium steady states…

Statistical Mechanics · Physics 2019-09-23 Hyungjoon Soh , Meesoon Ha

Consider the stationary measure of open asymmetric simple exclusion process (ASEP) on the lattice $\{1,\dots,n\}$. Taking $n$ to infinity while fixing the jump rates, this measure converges to a measure on the semi-infinite lattice. In the…

Probability · Mathematics 2025-10-23 Zongrui Yang

We study an interacting particle process on a finite ring with $L$ sites with at most $K$ particles per site, in which particles hop to nearest neighbors with rates given in terms of $t$-deformed integers and asymmetry parameter $q$, where…

Statistical Mechanics · Physics 2025-06-17 Arvind Ayyer , Samarth Misra

We investigate the splitting probability of a monitored continuous-time quantum walk with two targets and show that, in stark contrast to a classical random walk, it exhibits a nonanalytic, phase-transition-like behavior controlled by the…

Statistical Mechanics · Physics 2026-01-23 Prashant Singh , David A. Kessler , Eli Barkai

For the symmetric simple exclusion process on an infinite line, we calculate exactly the fluctuations of the integrated current $Q_t$ during time $t$ through the origin when, in the initial condition, the sites are occupied with density…

Statistical Mechanics · Physics 2015-05-13 Bernard Derrida , Antoine Gerschenfeld

We obtain a new relation between the distributions $\mu_t$ at different times $t\ge 0$ of the continuous-time TASEP (Totally Asymmetric Simple Exclusion Process) started from the step initial configuration. Namely, we present a…

Probability · Mathematics 2021-02-18 Leonid Petrov , Axel Saenz

The TASEP is a paradigmatic model of out-of-equilibrium statistical physics, for which many quantities have been computed, either exactly or by approximate methods. In this work we study two new kinds of observables that have some relevance…

Statistical Mechanics · Physics 2017-09-20 Julien Cividini , Cécile Appert-Rolland

We consider the fluctuations of the largest eigenvalue of sparse random matrices, the class of random matrices that includes the normalized adjacency matrices of the Erd\H{o}s-R\'enyi graph $G(N, p)$. We show that the fluctuations of the…

Probability · Mathematics 2025-07-28 Teodor Bucht , Kevin Schnelli , Yuanyuan Xu

While originally discovered in the context of the Gaussian Unitary Ensemble, the Tracy-Widom distribution also rules the height fluctuations of growth processes. This suggests that there might be other nonequilibrium processes in which the…

Statistical Mechanics · Physics 2016-06-07 Christian B. Mendl , Herbert Spohn

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

We study a generalization of the asymmetric simple inclusion process (ASIP) on a periodic one-dimensional lattice, where the integers in the particles rates are deformed to their $t$-analogues. We call this the $(q, t, \theta)$~ASIP, where…

Statistical Mechanics · Physics 2025-10-13 Arvind Ayyer , Samarth Misra

We consider sample covariance matrices of the form $\mathcal{Q}=(\Sigma^{1/2}X)(\Sigma^{1/2} X)^*$, where the sample $X$ is an $M\times N$ random matrix whose entries are real independent random variables with variance $1/N$ and where…

Probability · Mathematics 2015-06-10 Ji Oon Lee , Kevin Schnelli

The totally asymmetric simple exclusion process in discrete time is considered on finite rings with fixed number of particles. A translation-invariant version of the backward-ordered sequential update is defined for periodic boundary…

Soft Condensed Matter · Physics 2007-05-23 J. G. Brankov , Vl. V. Papoyan , V. S. Poghosyan , V. B. Priezzhev

In this paper, we study the largest eigenvalues of sample covariance matrices with elliptically distributed data. We consider the sample covariance matrix $Q=YY^*,$ where the data matrix $Y \in \mathbb{R}^{p \times n}$ contains i.i.d.…

Probability · Mathematics 2023-04-24 Xiucai Ding , Jiahui Xie