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

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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

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

We examine height-height correlations in the transient growth regime of the 2+1 Kardar-Parisi-Zhang (KPZ) universality class, with a particular focus on the {\it spatial covariance} of the underlying two-point statistics, higher-dimensional…

Statistical Mechanics · Physics 2014-03-31 T. Halpin-Healy , G. Palasantzas

This article presents some methods to control the bottom of the spectrum of the Laplacian $\lambda_0$ on hyperbolic surfaces with infinite volume. Our first result bounds the $\lambda_0$ of a geometrically finite surface in terms of the…

Differential Geometry · Mathematics 2008-07-28 Samuel Tapie

Motivated by the recent exact solution of the {\it stationary-state} Kardar-Parisi-Zhang (KPZ) statistics by Imamura & Sasamoto (Phys. Rev. Lett. {\bf 108}, 190603 (2012)), as well as a precursor experimental signature unearthed by Takeuchi…

Statistical Mechanics · Physics 2014-03-31 Timothy Halpin-Healy , Yuexia Lin

The Kardar-Parisi-Zhang (KPZ) equation has been connected to a large number of important stochastic processes in physics, chemistry and growth phenomena, ranging from classical to quantum physics. The central quest in this field is the…

Statistical Mechanics · Physics 2021-12-01 Márcio S. Gomes-Filho , André L. A. Penna , Fernando A. Oliveira

We consider an infinite interface in $d>2$ dimensions, governed by the Kardar-Parisi-Zhang (KPZ) equation with a weak Gaussian noise which is delta-correlated in time and has short-range spatial correlations. We study the probability…

Statistical Mechanics · Physics 2018-05-02 Baruch Meerson , Pavel V. Sasorov , Arkady Vilenkin

We study the diffusion phenomena on the negatively curved surface made up of congruent heptagons. Unlike the usual two-dimensional plane, this structure makes the boundary increase exponentially with the distance from the center, and hence…

Statistical Mechanics · Physics 2008-07-15 Seung Ki Baek , Su Do Yi , Beom Jun Kim

We propose a mean field theory for interfaces growing according to the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions. The mean field equations are formulated in terms of densities at different heights, taking surface tension and the…

Statistical Mechanics · Physics 2009-11-10 Francesco Ginelli , Haye Hinrichsen

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

In this paper we consider a generalized diffusion equation on a square lattice corresponding to Mellin transforms of the $k$-path Laplacian. In particular, we prove that superdiffusion occurs when the parameter $s$ in the Mellin transform…

Functional Analysis · Mathematics 2018-07-10 Ernesto Estrada , Ehsan Hameed , Matthias Langer , Aleksandra Puchalska

We study coupled KPZ equations with three control parameters $X,Y,T$. These equations are used in the context of stretched polymers in a random medium, for the spacetime spin-spin correlator of the isotropic quantum Heisenberg chain, and…

Statistical Mechanics · Physics 2025-06-03 Dipankar Roy , Abhishek Dhar , Manas Kulkarni , Herbert Spohn

We study the spectral dimension associated with diffusion processes on Euclidean $\kappa$-Minkowski space. We start by describing a geometric construction of the "Euclidean" momentum group manifold related to $\kappa$-Minkowski space. On…

High Energy Physics - Theory · Physics 2014-06-25 Michele Arzano , Tomasz Trzesniewski

Recent approximate analytical work has suggested that, at certain values of the external pump, the optical parametric oscillator (OPO) regime of microcavity polaritons may provide a long sought realisation of Kardar-Parisi-Zhang (KPZ)…

Quantum Gases · Physics 2022-05-09 A. Ferrier , A. Zamora , G. Dagvadorj , M. H. Szymańska

A perturbative method is developed to calculate the finite size corrections of the low lying energies of the asymmetric XXZ hamiltonian near the stochastic line. The crossover from isotropic to anisotropic, Kardar-Parisi-Zhang (KPZ) scaling…

Condensed Matter · Physics 2008-02-03 Doochul Kim

This paper studies the large scale limits of multi-type invariant distributions and Busemann functions of planar stochastic growth models in the Kardar-Parisi-Zhang (KPZ) class. We identify a set of sufficient hypotheses for convergence of…

Probability · Mathematics 2025-02-06 Ofer Busani , Timo Seppäläinen , Evan Sorensen

It is shown that when $d\ge 3$, the growing random surface generated by the $(d+1)$-dimensional directed polymer model at sufficiently high temperature, after being smoothed by taking microscopic local averages, converges to a solution of…

Probability · Mathematics 2022-05-16 Sourav Chatterjee

Over the past years our understanding of the scaling properties of the solutions to the one-dimensional KPZ equation has advanced considerably, both theoretically and experimentally. In our contribution we export these insights to the case…

Statistical Mechanics · Physics 2016-10-24 Patrik L. Ferrari , Tomohiro Sasamoto , Herbert Spohn

Extensive dynamical simulations of Restricted Solid on Solid models in $D=2+1$ dimensions have been done using parallel multisurface algorithms implemented on graphics cards. Numerical evidence is presented that these models exhibit KPZ…

Statistical Mechanics · Physics 2016-08-08 Jeffrey Kelling , Géza Ódor , Sibylle Gemming

We study a restricted solid-on-solid (RSOS) model involving deposition and evaporation with probabilities p and 1-p, respectively, in one-dimensional substrates. It presents a crossover from Edwards-Wilkinson (EW) to Kardar-Parisi-Zhang…

Statistical Mechanics · Physics 2014-05-07 T. J. Oliveira , K. Dechoum , J. A. Redinz , F. D. A. Aarao Reis