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Related papers: Universal fluctuations in KPZ growth on one-dimens…

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In [arXiv:0804.3035] we studied an interacting particle system which can be also interpreted as a stochastic growth model. This model belongs to the anisotropic KPZ class in 2+1 dimensions. In this paper we present the results that are…

Statistical Mechanics · Physics 2012-10-29 Patrik L. Ferrari , Alexei Borodin

We study effects of turbulent mixing on the random growth of an interface in the problem of the deposition of a substance on a substrate. The growth is modelled by the well-known Kardar--Parisi--Zhang model. The turbulent advecting velocity…

Statistical Mechanics · Physics 2015-11-06 N. V. Antonov , P. I. Kakin

The front of a compact bacterial colony growing on a Petri dish is a paradigmatic instance of non-equilibrium fluctuations in the celebrated Eden, or Kardar-Parisi-Zhang (KPZ), universality class. While in many experiments the scaling…

We study numerically the kinetic roughening properties of the precursor fronts of nonvolatile liquid droplets spreading on solid substrates, for the case of circular droplets, more frequently addressed in experiments. To this end, we…

Statistical Mechanics · Physics 2025-04-24 J. M. Marcos , J. J. Melendez , R. Cuerno , J. J. Ruiz-Lorenzo

In this contribution we consider stochastic growth models in the Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large time distribution and processes and their dependence on the class on initial condition. This…

Mathematical Physics · Physics 2011-03-01 Patrik L. Ferrari

In this study, we investigate the relationship between the one-dimensional (1D) Kardar-Parisi-Zhang (KPZ) equation and the stochastic Loewner equation (SLE), which is a one parameter family of the conformal mappings involving stochasticity.…

Statistical Mechanics · Physics 2026-04-07 Yusuke Kosaka Shibasaki

Tracking the sign of fluctuations governed by the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) universality class, we show, both experimentally and numerically, that its evolution has an unexpected link to a simple stochastic model called…

Statistical Mechanics · Physics 2016-08-17 Kazumasa A. Takeuchi , Takuma Akimoto

We have studied front dynamics for the discrete $A+A \leftrightarrow A$ reaction-diffusion system, which in the continuum is described by the (stochastic) Fisher-Kolmogorov-Petrovsky-Piscunov equation. We have revisited this discrete model…

Statistical Mechanics · Physics 2023-11-30 B. G. Barreales , J. J. Melendez , R. Cuerno , J. J. Ruiz-Lorenzo

We study the joint probability distribution function (pdf) of the maximum M of the height and its position X_M of a curved growing interface belonging to the universality class described by the Kardar-Parisi-Zhang equation in 1+1…

Statistical Mechanics · Physics 2015-05-18 Joachim Rambeau , Gregory Schehr

We study the kinetic roughening of the single-step (SS) growth model with a tunable parameter $p$ in $1+1$ and $2+1$ dimensions by performing extensive numerical simulations. We show that there exists a very slow crossover from an…

Statistical Mechanics · Physics 2020-06-09 E. Daryaei

We consider the Kardar-Parisi-Zhang (KPZ) fixed point $\mathrm{H}(x,\tau)$ with the narrow-wedge initial condition and investigate the distribution of $\mathrm{H}(x,\tau)$ conditioned on a large height at an earlier space-time point…

Probability · Mathematics 2025-02-28 Ron Nissim , Ruixuan Zhang

We consider the polynuclear growth (PNG) model in 1+1 dimension with flat initial condition and no extra constraints. Through the Robinson-Schensted-Knuth (RSK) construction, one obtains the multilayer PNG model, which consists of a stack…

Mathematical Physics · Physics 2007-05-23 Patrik L. Ferrari

Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its properties (such as distribution functions or regularity) and expanding the breadth of its…

Probability · Mathematics 2011-11-03 Ivan Corwin

We investigate analytically the large dimensional behavior of the Kardar-Parisi-Zhang (KPZ) dynamics of surface growth using a recently proposed non-perturbative renormalization for self-affine surface dynamics. Within this framework, we…

Statistical Mechanics · Physics 2009-10-31 C. Castellano , A. Gabrielli , M. Marsili , M. A. Munoz , L. Pietronero

We introduce a class of (2+1)-dimensional stochastic growth processes, that can be seen as irreversible random dynamics of discrete interfaces. "Irreversible" means that the interface has an average non-zero drift. Interface configurations…

Probability · Mathematics 2017-09-26 Fabio Lucio Toninelli

We have used kinetic Monte Carlo (kMC) simulations of a lattice gas to study front fluctuations in the spreading of a non-volatile liquid droplet onto a solid substrate. Our results are consistent with a diffusive growth law for the radius…

Statistical Mechanics · Physics 2023-11-30 J. M. Marcos , P. Rodríguez-López , J. J. Melendez , R. Cuerno , J. J. Ruiz-Lorenzo

We show that d+1-dimensional surface growth models can be mapped onto driven lattice gases of d-mers. The continuous surface growth corresponds to one dimensional drift of d-mers perpendicular to the (d-1)-dimensional "plane" spanned by the…

Statistical Mechanics · Physics 2014-01-21 Geza Odor , Bartosz Liedke , Karl-Heinz Heinig

The KPZ fixed point is a scaling invariant Markov process which arises as the universal scaling limit of a broad class of models of random interface growth in one dimension, the one-dimensional KPZ universality class. In this survey we…

Probability · Mathematics 2022-05-04 Daniel Remenik

The power spectrum of interface fluctuations in the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) universality class is studied both experimentally and numerically. The $1/f^\alpha$-type spectrum is found and characterized through a set of…

Statistical Mechanics · Physics 2017-06-09 Kazumasa A. Takeuchi

Exciton-polaritons under driven-dissipative conditions exhibit a condensation transition which belongs to a different universality class than equilibrium Bose-Einstein condensates. By numerically solving the generalized Gross-Pitaevskii…

Statistical Mechanics · Physics 2018-06-06 Davide Squizzato , Léonie Canet , Anna Minguzzi