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Related papers: Finite time corrections in KPZ growth models

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We use the optimal fluctuation method to evaluate the short-time probability distribution $\mathcal{P}\left(H,L,t\right)$ of height at a single point, $H=h\left(x=0,t\right)$, of the evolving Kardar-Parisi-Zhang (KPZ) interface…

Statistical Mechanics · Physics 2018-02-15 Naftali R. Smith , Baruch Meerson , Pavel Sasorov

Universality is a well-established central concept of equilibrium physics. However, in systems far away from equilibrium a deeper understanding of its underlying principles is still lacking. Up to now, a few classes have been identified.…

Statistical Mechanics · Physics 2015-10-19 Vladislav Popkov , Andreas Schadschneider , Johannes Schmidt , Gunter M. Schütz

We present an analytical method, rooted in the non-perturbative renormalization group, that allows one to calculate the critical exponents and the correlation and response functions of the Kardar-Parisi-Zhang (KPZ) growth equation in all…

Statistical Mechanics · Physics 2015-05-28 Léonie Canet , Hugues Chaté , Bertrand Delamotte , Nicolás Wschebor

The determination of the exact exponents of the KPZ class in any substrate dimension $d$ is one of the most important open issues in Statistical Physics. Based on the behavior of the dimensional variation of some exact exponent differences…

Statistical Mechanics · Physics 2022-12-21 Tiago J. Oliveira

We study the fluctuations of the current J(t) of the totally asymmetric exclusion process with open boundaries. Using a density matrix renormalization group approach, we calculate the cumulant generating function of the current. This…

Statistical Mechanics · Physics 2015-05-20 Mieke Gorissen , Carlo Vanderzande

We consider time correlation for KPZ growth in 1+1 dimensions in a neighborhood of a characteristics. We prove convergence of the covariance with droplet, flat and stationary initial profile. In particular, this provides a rigorous proof of…

Mathematical Physics · Physics 2019-01-30 Patrik L. Ferrari , Alessandra Occelli

We study the last-passage growth model on the planar integer lattice with exponential weights. With boundary conditions that represent the equilibrium exclusion process as seen from a particle right after its jump we prove that the variance…

Probability · Mathematics 2007-06-13 Marton Balazs , Eric Cator , Timo Seppalainen

We discuss the universal behavior linked to the Goldstone mode associated with the spontaneous breaking of time-translation symmetry in many-body systems, in which the order parameter traces out a limit cycle. We show that this universal…

Statistical Mechanics · Physics 2025-08-04 Romain Daviet , Carl Philipp Zelle , Armin Asadollahi , Sebastian Diehl

The Kardar-Parisi-Zhang (KPZ) equation is conjectured to universally describe the fluctuations of weakly asymmetric interface growth. Here we provide the first intrinsic well-posedness result for the KPZ equation on the real line by showing…

Probability · Mathematics 2016-08-09 M. Gubinelli , N. Perkowski

The statistics of the fluctuations of quantum many-body systems are highly revealing of their nature. In driven-dissipative systems displaying macroscopic quantum coherence, as exciton polariton condensates under incoherent pumping, the…

We explore linear control of the one-dimensional non-linear Kardar--Parisi--Zhang (KPZ) equation with the goal to understand the effects the control process has on the dynamics and on the stationary state of the resulting stochastic growth…

Statistical Mechanics · Physics 2021-05-11 Priyanka , Uwe C Tauber , Michel Pleimling

I characterize the extreme location and extreme first passage time of a system of $N$ particles independently diffusing in a space-time random environment. I show these extreme statistics are governed by the Kardar-Parisi-Zhang (KPZ)…

Statistical Mechanics · Physics 2025-05-06 Jacob Hass

The Kardar-Parisi-Zhang (KPZ) equation of nonlinear stochastic growth in d dimensions is studied using the mapping onto a system of directed polymers in a quenched random medium. The polymer problem is renormalized exactly in a minimally…

Condensed Matter · Physics 2016-08-31 Michael Lassig

The celebrated Kardar-Parisi-Zhang (KPZ) equation describes the kinetic roughening of stochastically growing interfaces. In one dimension, the KPZ equation is exactly solvable and its statistical properties are known to an exquisite degree.…

Statistical Mechanics · Physics 2023-12-25 Côme Fontaine , Francesco Vercesi , Marc Brachet , Léonie Canet

We study the synchronization physics of 1D and 2D oscillator lattices subject to noise and predict a dynamical transition that leads to a sudden drastic increase of phase diffusion. Our analysis is based on the widely applicable…

Statistical Mechanics · Physics 2017-08-02 Roland Lauter , Aditi Mitra , Florian Marquardt

We obtain exact formulas for moments and generating functions of the height function of the asymmetric simple exclusion process at one spatial point, starting from special initial data in which every positive even site is initially…

Probability · Mathematics 2016-01-13 Janosch Ortmann , Jeremy Quastel , Daniel Remenik

We compute the growth fluctuations in equilibrium of a wide class of deposition models. These models also serve as general frame to several nearest-neighbor particle jump processes, e.g. the simple exclusion or the zero range process, where…

Probability · Mathematics 2007-09-12 Marton Balazs

We investigate the infinite-dimensional limit of nonequilibrium surface growth by numerically integrating stochastic growth equations on a fully connected graph. In particular, we study the Edwards-Wilkinson (EW), Kardar-Parisi-Zhang (KPZ),…

Statistical Mechanics · Physics 2026-03-04 J. M. Marcos , J. J. Meléndez , R. Cuerno , J. J. Ruiz-Lorenzo

The Kardar-Parisi-Zhang (KPZ) equation for surface growth has been analyzed for over three decades. Some experiments indicated the power law for the interface width, $w(t)\sim t^\beta$, remains the same as in growth on planar surfaces.…

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