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Related papers: Finite time corrections in KPZ growth models

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Ballistic deposition (BD) is considered to be a paradigmatic discrete growth model that represents the Kardar-Parisi-Zhang (KPZ) universality class. In this paper we question this connection by rigorously deriving a formal continuum…

Statistical Mechanics · Physics 2008-04-21 Eytan Katzav , Moshe Schwartz

We investigate the behavior of discrete interface growth models belonging to the Edwards--Wilkinson (EW) and Kardar--Parisi--Zhang (KPZ) universality classes, when defined on a complete graph, a topology commonly used to probe the…

Statistical Mechanics · Physics 2026-05-01 J. M. Marcos , J. J. Meléndez , R. Cuerno , J. J. Ruiz-Lorenzo

Temporal correlation for randomly growing interfaces in the KPZ universality class is a topic of recent interest. Most of the works so far have been concentrated on the zero temperature model of exponential last passage percolation, and…

Probability · Mathematics 2024-01-31 Riddhipratim Basu , Xiao Shen

Consider a deterministically growing surface of any dimension, where the growth at a point is an arbitrary nonlinear function of the heights at that point and its neighboring points. Assuming that this nonlinear function is monotone,…

Probability · Mathematics 2021-09-07 Sourav Chatterjee

We report a numerical analysis of corrections to finite size scaling at the Anderson transition due to irrelevant scaling variables and non-linearities of the scaling variables. By taking proper account of these corrections, the…

Disordered Systems and Neural Networks · Physics 2009-10-31 Keith Slevin , Tomi Ohtsuki

The early time regime of the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimension, starting from a Brownian initial condition with a drift $w$, is studied using the exact Fredholm determinant representation. For large drift we recover the…

Statistical Mechanics · Physics 2017-08-23 Alexandre Krajenbrink , Pierre Le Doussal

Considered are the large $N$, or large intensity, forms of the distribution of the length of the longest increasing subsequences for various models. Earlier work has established that after centring and scaling, the limit laws for these…

Mathematical Physics · Physics 2022-06-09 Peter J. Forrester , Anthony Mays

We introduce a collection of nonlinear integrable partial differential-difference equations that are satisfied by the one-point distribution functions of some classical integrable KPZ models. Moreover, these equations can be regarded as…

Probability · Mathematics 2025-09-23 C. Alexander Rodriguez

The nonequilibrium steady state of the one-dimensional (1D) Kardar-Parisi-Zhang (KPZ) universality class is studied in-depth by exact solutions, yet no direct experimental evidence of its characteristic statistical properties has been…

Statistical Mechanics · Physics 2020-07-14 Takayasu Iwatsuka , Yohsuke T. Fukai , Kazumasa A. Takeuchi

We consider the periodic totally asymmetric simple exclusion process with a general initial condition that properly approximates a periodic upper-semicontinuous function. We find the large time limit of the rescaled space-time multipoint…

Probability · Mathematics 2026-03-03 Jinho Baik , Yuchen Liao , Zhipeng Liu

The symmetric simple exclusion process is one of the simplest out-of-equilibrium systems for which the steady state is known. Its large deviation functional of the density has been computed in the past both by microscopic and macroscopic…

Statistical Mechanics · Physics 2015-06-15 B. Derrida , M. Retaux

We consider the stochastic six-vertex (S6V) model and asymmetric simple exclusion process (ASEP) under general initial conditions which are bounded below lines of arbitrary slope at $\pm\infty$. We show under Kardar-Parisi-Zhang (KPZ)…

Probability · Mathematics 2024-12-25 Amol Aggarwal , Ivan Corwin , Milind Hegde

We study the convergence and shape correction to the limit distributions of extreme values due to the finite size (FS) of data sets. A renormalization method is introduced for the case of independent, identically distributed (iid)…

Statistical Mechanics · Physics 2009-11-13 G. Gyorgyi , N. R. Moloney , K. Ozogany , Z. Racz

We propose Josephson junction arrays as realistic platforms for observing nonequilibrium scaling laws characterizing the Kardar-Parisi-Zhang (KPZ) universality class, and space-time soliton proliferation. Focusing on a two-chain ladder…

Statistical Mechanics · Physics 2025-12-12 Mikheil Tsitsishvili , Reinhold Egger , Karsten Flensberg , Sebastian Diehl

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 explore the Kardar-Parisi-Zhang (KPZ) scaling in the one-dimensional Hubbard model, which exhibits global $SU_c(2)\otimes SU_s(2)$ symmetry at half-filling, for the pseudo-charge and the total spin. We analyze dynamical scaling…

Strongly Correlated Electrons · Physics 2023-12-14 Cătălin Paşcu Moca , Miklós Antal Werner , Angelo Valli , Gergely Zaránd , Tomaž Prosen

We investigate the radius distributions (RD) of surfaces obtained with large-scale simulations of radial clusters that belong to the KPZ universality class. For all investigated models, the RDs are given by the Tracy-Widom distribution of…

Statistical Mechanics · Physics 2011-11-10 S. G. Alves , T. J. Oliveira , S. C. Ferreira

We study the role of the topology of the background space on the one-dimensional Kardar-Parisi-Zhang (KPZ) universality class. To do so, we study the growth of balls on disordered 2D manifolds with random Riemannian metrics, generated by…

Statistical Mechanics · Physics 2017-03-08 Silvia N. Santalla , Javier Rodriguez-Laguna , Alessio Celi , Rodolfo Cuerno

We have considered three different "one-body" statistical systems involving Brownian excursions, which possess for fluctuations Kardar-Parisi-Zhang scaling with the critical exponent $\nu=\frac{1}{3}$. In all models imposed external…

Statistical Mechanics · Physics 2020-05-07 Alexander Gorsky , Sergei Nechaev , Alexander Valov

Height fluctuations of growing surfaces can be characterized by the probability distribution of height in a spatial point at a finite time. Recently there has been spectacular progress in the studies of this quantity for the…

Statistical Mechanics · Physics 2017-01-25 Naftali R. Smith , Baruch Meerson , Pavel V. Sasorov