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Results of experiments on the dynamics and kinetic roughening of one-dimensional slow-combustion fronts in three grades of paper are reported. Extensive averaging of the data allows a detailed analysis of the spatial and temporal…

Statistical Mechanics · Physics 2009-11-07 M. Myllys , J. Maunuksela , M. Alava , T. Ala-Nissila , J. Merikoski , J. Timonen

We explain the relation between certain random tiling models and interacting particle systems belonging to the anisotropic KPZ (Kardar-Parisi-Zhang) universality class in 2+1-dimensions. The link between these two \emph{a priori} disjoint…

Mathematical Physics · Physics 2015-06-15 Alexei Borodin , Patrik L. Ferrari

Tracy-Widom and Baik-Rains distributions appear as universal limit distributions for height fluctuations in the one-dimensional Kardar-Parisi-Zhang (KPZ) \textit{stochastic} partial differential equation (PDE). We obtain the same universal…

Statistical Mechanics · Physics 2020-04-01 Dipankar Roy , Rahul Pandit

We consider the orientational diffusion controlled by the hyperspherical Laplacian, $\nabla^2_D$, on the surface of the $D$--dimensional hypersphere in the limit $D \to \infty$. We find that for stretched paths with lengths relatively short…

Statistical Mechanics · Physics 2024-12-11 Daniil Fedotov , Sergei Nechaev

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

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

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

Recently, a variational approach has been introduced for the paradigmatic Kardar--Parisi--Zhang (KPZ) equation. Here we review that approach, together with the functional Taylor expansion that the KPZ nonequilibrium potential (NEP) admits.…

Statistical Mechanics · Physics 2014-01-27 Horacio S. Wio , Roberto R. Deza , Carlos Escudero , Jorge A. Revelli

We study in the present article the Kardar-Parisi-Zhang (KPZ) equation $$ \partial_t h(t,x)=\nu\Delta h(t,x)+\lambda |\nabla h(t,x)|^2 +\sqrt{D}\, \eta(t,x), \qquad (t,x)\in\mathbb{R}_+\times\mathbb{R}^d $$ in $d\ge 3$ dimensions in the…

Analysis of PDEs · Mathematics 2018-01-24 Jacques Magnen , Jérémie Unterberger

We characterize universal features of the sample-to-sample fluctuations of global geometrical observables, such as the area, width, length, and center-of-mass position, in random growing planar clusters. Our examples are taken from…

Observing super-diffusive fluctuations from Kardar-Parisi-Zhang (KPZ) universality in isotropic integrable spin chains is usually challenging as it requires a fairly large number of spins in interaction. We demonstrate in this paper, in the…

Statistical Mechanics · Physics 2026-01-16 Sylvain Prolhac

In its original version the KPZ equation models the dynamics of an interface bordering a stable phase against a metastable one. Over past years the corresponding two-dimensional field theory has been applied to models with different…

Statistical Mechanics · Physics 2020-06-24 Herbert Spohn

We show that the emergence of different surface patterns (ripples, dots) can be well understood by a suitable mapping onto the simplest nonequilibrium lattice gases and cellular automata.Using this efficient approach difficult, unanswered…

Statistical Mechanics · Physics 2014-01-21 Géza Ódor , Bartosz Liedke , Karl-Heinz Heinig , Jeffrey Kelling

We identify the key features of Kardar-Parisi-Zhang universality class in the fluctuations of the wave density logarithm, in a two-dimensional Anderson localized wave packet. In our numerical analysis, the fluctuations are found to exhibit…

Disordered Systems and Neural Networks · Physics 2024-04-24 Sen Mu , Jiangbin Gong , Gabriel Lemarié

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

This paper concerns the multi-component coupled Kardar-Parisi-Zhang (KPZ) equation and its two types of approximations. One approximation is obtained as a simple replacement of the noise term by a smeared noise with a proper…

Probability · Mathematics 2017-03-30 Tadahisa Funaki , Masato Hoshino

We define a stochastic lattice model for a fluctuating directed polymer in $d\geq 2$ dimensions. This model can be alternatively interpreted as a fluctuating random path in 2 dimensions, or a one-dimensional asymmetric simple exclusion…

Statistical Mechanics · Physics 2017-09-20 G. M. Schütz , B. Wehefritz-Kaufmann

For stochastic growth models in the Kardar-Parisi-Zhang (KPZ) class in 1+1 dimensions, fluctuations grow as t^{1/3} during time t and the correlation length at a fixed time scales as t^{2/3}. In this note we discuss the scale of time…

Mathematical Physics · Physics 2008-11-01 Patrik L. Ferrari

We present a lattice gas model that without fine tuning of parameters is expected to exhibit the so far elusive modified Kardar-Parisi-Zhang (KPZ) universality class. To this end, we review briefly how non-linear fluctuating hydrodynamics…

Probability · Mathematics 2017-10-26 Gunter M. Schütz

In the universality class of the one dimensional Kardar-Parisi-Zhang surface growth, Derrida and Lebowitz conjectured the universality of not only the scaling exponents, but of an entire scaling function. Since Derrida and Lebowitz's…

Statistical Mechanics · Physics 2009-11-11 Nicholas Chia , Ralf Bundschuh