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Related papers: Anisotropic growth of random surfaces in 2+1 dimen…

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In [arXiv:0804.3035] we studied an interacting particle system which can be also interpreted as a stochastic growth model. This model belongs to the anisotropic KPZ class in 2+1 dimensions. In this paper we present the results that are…

Statistical Mechanics · Physics 2012-10-29 Patrik L. Ferrari , Alexei Borodin

We introduce a self-organized surface growth model in 2+1 dimensions with anisotropic avalanche process, which is expected to be in the universality class of the anisotropic quenched Kardar-Parisi-Zhang equation with alternative signs of…

Statistical Mechanics · Physics 2009-10-28 HaWoong Jeong , ByungNam Kahng , Doochul Kim

Stochastic growth processes in dimension $(2+1)$ were conjectured by D. Wolf, on the basis of renormalization-group arguments, to fall into two distinct universality classes, according to whether the Hessian $H_\rho$ of the speed of growth…

Probability · Mathematics 2020-03-25 Sunil Chhita , Fabio Lucio Toninelli

Stochastic interface dynamics serve as mathematical models for diverse time-dependent physical phenomena: the evolution of boundaries between thermodynamic phases, crystal growth, random deposition... Interesting limits arise at large…

Probability · Mathematics 2019-03-22 F. L. Toninelli

While the 1-point height distributions (HDs) and 2-point covariances of $(2+1)$ KPZ systems have been investigated in several recent works for flat and spherical geometries, for the cylindrical one the HD was analyzed for few models and…

Statistical Mechanics · Physics 2023-06-29 Ismael S. S. Carrasco , Tiago J. Oliveira

We consider a discrete model for anisotropic (2+1)-dimensional growth of an interface height function. Owing to a connection with q-Whittaker functions, this system enjoys many explicit integral formulas. By considering certain Gaussian…

Probability · Mathematics 2018-05-02 Alexei Borodin , Ivan Corwin , Patrik L. Ferrari

A series of recent works focused on two-dimensional interface growth models in the so-called Anisotropic KPZ (AKPZ) universality class, that have a large-scale behavior similar to that of the Edwards-Wilkinson equation. In agreement with…

Mathematical Physics · Physics 2020-09-29 Alexei Borodin , Fabio Lucio Toninelli

The domino-shuffling algorithm can be seen as a stochastic process describing the irreversible growth of a $(2+1)$-dimensional discrete interface. Its stationary speed of growth $v_{\mathtt w}(\rho)$ depends on the average interface slope…

Probability · Mathematics 2021-08-27 Sunil Chhita , Fabio Lucio Toninelli

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 introduce a class of (2+1)-dimensional stochastic growth processes, that can be seen as irreversible random dynamics of discrete interfaces. "Irreversible" means that the interface has an average non-zero drift. Interface configurations…

Probability · Mathematics 2017-09-26 Fabio Lucio Toninelli

Long-range spatiotemporal correlations may play important roles in nonequilibrium surface growth process. In order to investigate the effects of long-range temporal correlation on dynamic scaling of growing surfaces, we perform extensive…

Statistical Mechanics · Physics 2021-08-11 Tianshu Song , Hui Xia

We generalize the surface growth model of Gates and Westcott to arbitrary inclination. The exact steady growth velocity is of saddle type with principal curvatures of opposite sign. According to Wolf this implies logarithmic height…

Statistical Mechanics · Physics 2009-10-28 M. Praehofer , H. Spohn

We determine a $q\to 1$ limit of the two-dimensional $q$-Whittaker driven particle system on the torus studied previously in [Corwin-Toninelli, arXiv:1509.01605]. This has an interpretation as a $(2+1)$-dimensional stochastic interface…

Probability · Mathematics 2018-06-28 Alexei Borodin , Ivan Corwin , Fabio Lucio Toninelli

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 consider a model of interface growth in two dimensions, given by a height function on the sites of the one--dimensional integer lattice. According to the discrete time update rule, the height above the site $x$ increases to the height…

Probability · Mathematics 2007-05-23 Janko Gravner , Craig A. Tracy , Harold Widom

We consider the multi-time correlation and covariance structure of a random surface growth with a wall introduced in arXiv:0904.2607. It is shown that the correlation functions associated with the model along space-like paths have…

Probability · Mathematics 2022-03-31 Zhengye Zhou

We consider the polynuclear growth (PNG) model in 1+1 dimension with flat initial condition and no extra constraints. The joint distributions of surface height at finitely many points at a fixed time moment are given as marginals of a…

Mathematical Physics · Physics 2010-03-09 Alexei Borodin , Patrik L. Ferrari , Tomohiro Sasamoto

We consider driven dimer models on the square and honeycomb graphs, starting from a stationary Gibbs measure. Each model can be thought of as a two dimensional stochastic growth model of an interface, belonging to the anisotropic KPZ…

Probability · Mathematics 2020-03-25 Sunil Chhita , Patrik L. Ferrari , Fabio Lucio Toninelli

We consider a large class of $1+1$-dimensional continuous interface growth models and we show that, in both the weakly asymmetric and the intermediate disorder regimes, these models converge to Hopf-Cole solutions to the KPZ equation.

Mathematical Physics · Physics 2015-12-25 Martin Hairer , Jeremy Quastel

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
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