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The growth of stochastic interfaces in the vicinity of a boundary and the non-trivial crossover towards the behaviour deep in the bulk is analysed. The causal interactions of the interface with the boundary lead to a roughness larger near…

Statistical Mechanics · Physics 2014-10-16 Nicolas Allegra , Jean-Yves Fortin , Malte Henkel

We develop a phenomenological mapping between submonolayer polynuclear growth (PNG) and the interface dynamics at and below the depinning transition in the Kardar-Parisi-Zhang equation for a negative non-linearity \lambda. This is possible…

Disordered Systems and Neural Networks · Physics 2009-11-07 Gabor J. Szabo , Mikko J. Alava

A geometric p-rough path can be seen to be a genuine path of finite p-variation with values in a Lie group equipped with a natural distance. The group and its distance lift (R^{d},+,0) and its Euclidean distance. This approach allows us to…

Probability · Mathematics 2007-05-23 Peter Friz , Nicolas Victoir

We describe a directed avalanche model; a slowly unloading sandbox driven by lowering a retaining wall. The directness of the dynamics allows us to interpret the stable sand surfaces as world sheets of fluctuating interfaces in one lower…

Statistical Mechanics · Physics 2009-11-07 Chun-Chung Chen , Marcel den Nijs

Burgers-Kardar-Parisi-Zhang (KPZ) scaling has recently (re-) surfaced in a variety of physical contexts, ranging from anharmonic chains to quantum systems such as open superfluids, in which a variety of random forces may be encountered…

Statistical Mechanics · Physics 2015-03-24 Philipp Strack

We study the competitive RSOS-BD model focusing on the validity of the Kardar-Parisi-Zhang (KPZ) ansatz h(t) = v t + (\Gamma t)^{\beta} \chi and the universality of the height distributions (HDs) near the point where the model has…

Statistical Mechanics · Physics 2013-03-14 Tiago J. Oliveira

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 Kardar-Parisi-Zhang (KPZ) equation sets the universality class for growing and roughening of nonequilibrium surfaces without any conservation law and nonlocal effects. We argue here that the KPZ equation can be generalized by including…

Statistical Mechanics · Physics 2025-12-01 Debayan Jana , Astik Haldar , Abhik Basu

We consider the evolution of interfaces with a diffusive term and a generalized Kardar-Parisi-Zhang (KPZ) non-linearity, which results in a propagation velocity that depends periodically on the tilt of the interface. Using large scale…

Statistical Mechanics · Physics 2022-01-06 Peter Grassberger

We analyze simulations results of a model proposed for etching of a crystalline solid and results of other discrete models in the 2+1-dimensional Kardar-Parisi-Zhang (KPZ) class. In the steady states, the moments W_n of orders n=2,3,4 of…

Statistical Mechanics · Physics 2009-11-10 Fabio D. A. Aarao Reis

Control of generically scale-invariant systems, i.e., targeting specific cooperative features in non-linear stochastic interacting systems with many degrees of freedom subject to strong fluctuations and correlations that are characterized…

Statistical Mechanics · Physics 2020-02-05 Priyanka , Uwe C. Täuber , Michel Pleimling

We develop a general universality technique for establishing metric scaling limits of critical random discrete structures exhibiting mean-field behavior that requires four ingredients: (i) from the barely subcritical regime to the critical…

Probability · Mathematics 2024-06-21 Jnaneshwar Baslingker , Shankar Bhamidi , Nicolas Broutin , Sanchayan Sen , Xuan Wang

We show that the increments of the KPZ fixed point started from arbitrary initial data are \emph{mutually} absolutely continuous with respect to Brownian motion with diffusion parameter $2$ on compacts, extending the one-sided Brownian…

Probability · Mathematics 2026-04-07 Pantelis Tassopoulos , Sourav Sarkar

We study a $(2+1)$-dimensional stochastic interface growth model, that is believed to belong to the so-called Anisotropic KPZ (AKPZ) universality class [Borodin and Ferrari, 2014]. It can be seen either as a two-dimensional interacting…

Probability · Mathematics 2017-04-24 Martin Legras , Fabio Lucio Toninelli

The Kardar-Parisi-Zhang (KPZ) universality class describes the coarse-grained behavior of a wealth of classical stochastic models. Surprisingly, it was recently conjectured to also describe spin transport in the one-dimensional quantum…

We consider point to point last passage times to every vertex in a neighbourhood of size $\delta N^{\frac{2}{3}}$, distance $N$ away from the starting point. The increments of these last passage times in this neighbourhood are shown to be…

Probability · Mathematics 2021-03-17 Márton Balázs , Ofer Busani , Timo Seppäläinen

We study the ballistic deposition and the grain deposition models on two-dimensional substrates. Using the Kardar-Parisi-Zhang (KPZ) ansatz for height fluctuations, we show that the main contribution to the intrinsic width, which causes…

Statistical Mechanics · Physics 2014-11-24 Sidiney G. Alves , Tiago J. Oliveira , Silvio C. Ferreira

The statistics of the average height fluctuation of the one-dimensional Kardar-Parisi-Zhang(KPZ)-type surface is investigated. Guided by the idea of local stationarity, we derive the scaling form of the characteristic function in the…

Statistical Mechanics · Physics 2009-11-11 Deok-Sun Lee , Doochul Kim

Scale-invariant fluctuations of growing interfaces are studied for circular clusters of an off-lattice variant of the Eden model, which belongs to the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) universality class. Statistical properties of…

Statistical Mechanics · Physics 2012-05-15 Kazumasa A. Takeuchi

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