English
Related papers

Related papers: The KPZ Universality Class and Related Topics

200 papers

The short-time evolution of a growing interface is studied analytically and numerically for the Kadar-Parisi-Zhang (KPZ) universality class. The scaling behavior of response and correlation functions is reminiscent of the ``initial slip''…

Statistical Mechanics · Physics 2009-10-30 M. Krech

Scanning probe microscopy (SPM) is a fundamental technique for the analysis of surfaces. In the present work, the interface statistics of surfaces scanned with a probe tip was analyzed for both \textit{in silico} and experimental systems…

Statistical Mechanics · Physics 2016-09-20 Sidiney G. Alves , Clodoaldo I. L. de Araujo , Silvio C. Ferreira

In this work, we present the multi-point probability distribution of the totally asymmetric simple exclusion process (TASEP) in a half-space, starting from a general deterministic initial condition. More precisely, let $h(t,x)$ denote the…

Probability · Mathematics 2025-08-08 Xincheng Zhang

We show that under the 1:2:3 scaling, critically probing large space and time, the height function of finite range asymmetric exclusion processes and the KPZ equation converge to the KPZ fixed point, constructed earlier as a limit of the…

Probability · Mathematics 2025-05-09 Jeremy Quastel , Sourav Sarkar

We study time-dependent density fluctuations in the stationary state of driven diffusive systems with two conserved densities $\rho_\lambda$. Using Monte-Carlo simulations of two coupled single-lane asymmetric simple exclusion processes we…

Statistical Mechanics · Physics 2016-08-08 V. Popkov , J. Schmidt , G. M. Schütz

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

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

In this paper, we discuss possible qualitative approaches to the problem of KPZ universality. Throughout the paper, our point of view is based on the geometrical and dynamical properties of minimisers and shocks forming interlacing…

Mathematical Physics · Physics 2018-03-14 Yuri Bakhtin , Konstantin Khanin

We consider the asymmetric simple exclusion process (ASEP) on $\mathbb{Z}$. For continuous densities, ASEP is in local equilibrium for large times, at discontinuities however, one expects to see a dynamical phase transition, i.e. a mixture…

Probability · Mathematics 2021-05-05 Peter Nejjar

This paper has two main goals. The first is universality of the KPZ equation for fluctuations of dynamic interfaces associated to interacting particle systems in the presence of open boundary. We consider generalizations on the open-ASEP…

Probability · Mathematics 2022-04-18 Kevin Yang

Despite similarities between models exhibiting absorbing phase transitions (APTs) and those showing Kardar-Parisi-Zhang (KPZ) growth, the relationship between these universal fluctuations has remained elusive. We numerically study…

Statistical Mechanics · Physics 2026-05-19 Yohsuke T. Fukai , Keiichi Tamai , Tetsuya Hiraiwa

We re-examine mode-coupling theory for the Kardar-Parisi-Zhang (KPZ) equation in the strong coupling limit and show that there exists two branches of solutions. One branch (or universality class) only exists for dimensionalities $d<d_c=2$…

Statistical Mechanics · Physics 2009-11-11 L. Canet , M. A. Moore

We consider universal aspects of two problems: (i) the slow purification of a large number of qubits by repeated quantum measurements, and (ii) the singular value structure of a product ${m_t m_{t-1}\ldots m_1}$ of many large random…

Statistical Mechanics · Physics 2024-06-21 Andrea De Luca , Chunxiao Liu , Adam Nahum , Tianci Zhou

We consider two versions of discrete time totally asymmetric simple exclusion processes (TASEPs) with geometric and Bernoulli random hopping probabilities. For the process mixed with these and continuous time dynamics, we obtain a single…

Mathematical Physics · Physics 2020-08-26 Yuta Arai

We analyze a class of non-simple exclusion processes and the corresponding growth models by generalizing Gaertners Cole-Hopf transformation. We identify the main non-linearity and eliminate it by imposing a gradient type condition. For…

Probability · Mathematics 2015-12-11 Amir Dembo , Li-Cheng Tsai

We study the effect of generic spatial anisotropies on the scaling behavior in the Kardar-Parisi-Zhang equation. In contrast to its "conserved" variants, anisotropic perturbations are found to be relevant in d > 2 dimensions, leading to…

Statistical Mechanics · Physics 2009-11-07 Uwe C. Tauber , E. Frey

The universality of the directed polymer model and the analogous KPZ equation is supported by numerical simulations using non-Gaussian random probability distributions in two, three and four dimensions. It is shown that although in the…

Disordered Systems and Neural Networks · Physics 2016-08-31 Ehud Perlsman , Shlomo Havlin

The totally asymmetric simple exclusion process (TASEP) is a stochastic model for the unidirectional flow of interacting particles on a 1D-lattice that is much used in systems biology and statistical physics. Its master equation describes…

Dynamical Systems · Mathematics 2026-04-20 Kilian Pioch , Lars Grüne , Thomas Kriecherbauer , Michael Margaliot

The Kardar-Parisi-Zhang (KPZ) equation has been connected to a large number of important stochastic processes in physics, chemistry and growth phenomena, ranging from classical to quantum physics. The central quest in this field is the…

Statistical Mechanics · Physics 2021-12-01 Márcio S. Gomes-Filho , André L. A. Penna , Fernando A. Oliveira

We conjecture the universal probability distribution at large time for the one-point height in the 1D Kardar-Parisi-Zhang (KPZ) stochastic growth universality class, with initial conditions interpolating from any one of the three main…

Statistical Mechanics · Physics 2017-06-07 Pierre Le Doussal