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Related papers: Local KPZ behavior under arbitrary scaling limits

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Kinetic roughening of a randomly growing surface can be modelled by the Kardar-Parisi-Zhang equation with a time-independent (``spatially quenched'' or ``columnar'') random noise. In this paper, we use the field-theoretic renormalization…

Statistical Mechanics · Physics 2023-12-15 N. V. Antonov , P. I. Kakin , M. A. Reiter

Recent theoretical studies have gradually deepened our understanding of the one-dimensional (1D) Kardar-Parisi-Zhang (KPZ) universality class even in the large deviation regime, but numerical methods for studying KPZ large deviations remain…

Statistical Mechanics · Physics 2026-02-09 Yuta Yanagibashi , Kazumasa A. Takeuchi

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

Synchronization in one dimension displays generic scale invariance with universal properties previously observed in surface kinetic roughening and the wider context of the Kardar-Parisi-Zhang (KPZ) universality class. This has been…

Statistical Mechanics · Physics 2026-04-08 Ricardo Gutierrez , Rodolfo Cuerno

Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang (KPZ) scaling in late-time correlators and autocorrelators of certain interacting many-body systems has been reported. Inspired by these results, we explore the KPZ scaling in…

High Energy Physics - Theory · Physics 2024-06-06 Alexander Gorsky , Sergei Nechaev , Alexander Valov

While stretching of a polymer along a flat surface is hardly different from the classical Pincus problem of pulling chain ends in free space, the role of curved geometry in conformational statistics of the stretched chain is an exciting…

Soft Condensed Matter · Physics 2022-08-30 Kirill E. Polovnikov , Sergei K. Nechaev , Alexander Y. Grosberg

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

We report on the effect of substrate temperature (T) on both local structure and long-wavelength fluctuations of polycrystalline CdTe thin films deposited on Si(001). A strong T-dependent mound evolution is observed and explained in terms…

Statistical Mechanics · Physics 2015-02-27 R. A. L. Almeida , S. O. Ferreira , I. R. B. Ribeiro , T. J. Oliveira

In this paper various predictions for the scaling exponents of the Nonlocal Kardar-Parisi-Zhang (NKPZ) equation are discussed. I use the Self-Consistent Expansion (SCE), and obtain results that are quite different from result obtained in…

Materials Science · Physics 2013-05-29 Eytan Katzav

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 main goal of this paper is to prove existence and non-existence results for deterministic Kardar-Parisi-Zhang type equations involving non-local "gradient terms". More precisely, let $\Omega \subset \mathbb{R}^N$, $N \geq 2$, be a…

Analysis of PDEs · Mathematics 2022-11-08 Boumediene Abdellaoui , Antonio J. Fernández , Tommaso Leonori , Abdelbadie Younes

Aiming to investigate the upper critical dimension, $d_u$, of the KPZ class, in [EPL 103 (2013) 10005] some growth models were numerically analyzed using Cayley trees (CTs) as substrates, as a way to access their behavior in the…

Statistical Mechanics · Physics 2021-03-31 Tiago J. Oliveira

We study the limit of a local average of the KPZ equation in dimension $d=2$ with general initial data in the subcritical regime. Our result shows that a proper spatial averaging of the KPZ equation converges in distribution to the sum of…

Probability · Mathematics 2024-01-01 Ran Tao

A growing interface subject to noise is described by the Kardar-Parisi-Zhang equation or, equivalently, the noisy Burgers equation. In one dimension this equation is analyzed by means of a weak noise canonical phase space approach applied…

Statistical Mechanics · Physics 2014-10-07 Hans C Fogedby

The dynamical regimes of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class are investigated in d=2+1 by extensive simulations considering flat and curved geometries. Geometry-dependent universal distributions, different…

Statistical Mechanics · Physics 2013-04-23 Tiago J. Oliveira , Sidiney G. Alves , Silvio C. Ferreira

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

We study the fourth order normalized cumulant of height fluctuations governed by $1+1$ dimensional Kardar-Parisi-Zhang (KPZ) equation for a growing surface. Following a diagrammatic renormalization scheme, we evaluate the kurtosis $Q$ from…

Statistical Mechanics · Physics 2015-11-19 Tapas Singha , Malay K. Nandy

In a recent paper, we exhibit a link between the average local growth of Laplace eigenfunctions on surfaces and the size of their nodal set. In that paper, the average local growth is computed using the uniform - or $L^\infty$ - growth…

Spectral Theory · Mathematics 2015-10-09 Guillaume Roy-Fortin

We present a comprehensive numerical investigation of non-universal parameters and corrections related to interface fluctuations of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class, in d=1+1, for both flat and curved…

Statistical Mechanics · Physics 2013-05-15 Sidiney G. Alves , Tiago J. Oliveira , Silvio C. Ferreira

Laplacian growth is the study of interfaces that move in proportion to harmonic measure. Physically, it arises in fluid flow and electrical problems involving a moving boundary. We survey progress over the last decade on discrete models of…

Probability · Mathematics 2016-11-03 Lionel Levine , Yuval Peres