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Related papers: KPZ-like scaling on a high-dimensional hypersphere

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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

In this article we study the scaling limit of the interface model on $\mathbb{Z}^d$ where the Hamiltonian is given by a mixed gradient and Laplacian interaction. We show that in any dimension the scaling limit is given by the Gaussian free…

Probability · Mathematics 2020-05-05 Alessandra Cipriani , Biltu Dan , Rajat Subhra Hazra

We consider a system of infinitely many interacting Brownian motions that models the height of a one-dimensional interface between two bulk phases. We prove that the large scale fluctuations of the system are well approximated by the…

Probability · Mathematics 2017-08-02 Joscha Diehl , Massimiliano Gubinelli , Nicolas Perkowski

We investigate solid-on-solid models that belong to the Kardar-Parisi-Zhang (KPZ) universality class on substrates that expand laterally at a constant rate by duplication of columns. Despite the null global curvature, we show that all…

Statistical Mechanics · Physics 2014-12-23 I. S. S. Carrasco , K. A. Takeuchi , S. C. Ferreira , T. J. Oliveira

We show that a 2+1 dimensional discrete surface growth model exhibiting Kardar-Parisi-Zhang (KPZ) class scaling can be mapped onto a two dimensional conserved lattice gas model of directed dimers. In case of KPZ height anisotropy the dimers…

Statistical Mechanics · Physics 2014-01-21 Geza Odor , Bartosz Liedke , Karl-Heinz Heinig

Equilibrium and nonequilibrium states of matter can exhibit fundamentally different behavior. A key example is the Kardar-Parisi-Zhang universality class in two spatial dimensions (2D KPZ), where microscopic deviations from equilibrium give…

We study a stochastic PDE model for an evolving set $\mathbb{M}(t)\subseteq\mathbb{R}^{\mathrm{d}+1}$ that resembles a continuum version of origin-excited or reinforced random walk. We show that long-time fluctuations of an associated…

Probability · Mathematics 2025-07-16 Amir Dembo , Kevin Yang

We show that the theoretical machinery developed for the Kardar-Parisi-Zhang (KPZ) class in low dimensions are obeyed by the restricted solid-on-solid (RSOS) model for substrates with dimensions up to $d=6$. Analyzing different restriction…

Statistical Mechanics · Physics 2014-08-26 Sidiney G. Alves , Tiago J. Oliveira , Silvio C. Ferreira

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

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…

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

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 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

The continuum Kardar-Parisi-Zhang equation in one dimension is lattice discretized in such a way that the drift part is divergence free. This allows to determine explicitly the stationary measures. We map the lattice KPZ equation to a…

Mathematical Physics · Physics 2015-05-13 Tomohiro Sasamoto , Herbert Spohn

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

Simulations of restricted solid-on-solid growth models are used to build the width-distributions of d=2-5 dimensional KPZ interfaces. We find that the universal scaling function associated with the steady-state width-distribution changes…

Statistical Mechanics · Physics 2009-11-07 E. Marinari , A. Pagnani , G. Parisi , Z. Racz

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

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

We simulate competitive two-component growth on a one dimensional substrate of $L$ sites. One component is a Poisson-type deposition that generates Kardar-Parisi-Zhang (KPZ) correlations. The other is random deposition (RD). We derive the…

Materials Science · Physics 2009-02-01 A. Kolakowska , M. A. Novotny , P. S. Verma

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