Steady-state skewness and kurtosis from renormalized cumulants in -dimensional stochastic surface growth
arXiv:1609.02547 · doi:10.1088/1742-5468/2016/10/103204
Abstract
The phenomenon of stochastic growth of a surface on a two-dimensional substrate occurs in Nature in a variety of circumstances and its statistical characterization requires the study of higher order cumulants. Here, we consider the statistical cumulants of height fluctuations governed by the -dimensional KPZ equation for flat geometry. We follow a diagrammatic scheme to derive the expressions for renormalized cumulants up to fourth order in the stationary state. Assuming a value for the roughness exponent from reliable numerical predictions, we calculate the second, third and fourth cumulants, yielding skewness and kurtosis . These values agree well with the available numerical estimations.
arXiv comment23 pages, 3 figures, version accepted in J. Stat. Mech. for publication
References in corpus (33)
- Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
- Universal Fluctuations of Growing Interfaces: Evidence in Turbulent Liquid Crystals
- Growing interfaces uncover universal fluctuations behind scale invariance
- A KPZ Cocktail- Shaken, not stirred: Toasting 30 years of kinetically roughened surfaces
- An exact solution for the KPZ equation with flat initial conditions
- Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
- Two-Loop Renormalization Group Analysis of the Burgers-Kardar-Parisi-Zhang Equation
- Exact solution for the stationary Kardar-Parisi-Zhang equation
- Critical Exponents of the KPZ Equation via Multi-Surface Coding Numerical Simulations
- Upper critical dimension, dynamic exponent and scaling functions in the mode-coupling theory for the Kardar-Parisi-Zhang equation
- Kinetic Roughening in Slow Combustion of Paper
- Nonlinear Measures for Characterizing Rough Surface Morphologies
- Extremely large scale simulation of a Kardar-Parisi-Zhang model using graphics cards
- Mode coupling and renormalization group results for the noisy Burgers equation
- Universal fluctuations in the growth of semiconductor thin films
- Universality in two-dimensional Kardar-Parisi-Zhang growth
- Universal correlators and distributions as experimental signatures of 2+1 Kardar-Parisi-Zhang growth
- Quantized Scaling of Growing Surfaces
- Numerical estimate of the Kardar Parisi Zhang universality class in (2 + 1) dimensions
- Nonperturbative renormalization group for the stationary Kardar-Parisi-Zhang equation: scaling functions and amplitude ratios in 1+1, 2+1 and 3+1 dimensions
- Similarity-Detection and Localization
- Crossover from Growing to Stationary Interfaces in the Kardar-Parisi-Zhang Class
- Numerical study of the Kardar-Parisi-Zhang equation
- Universality of fluctuations in the Kardar-Parisi-Zhang class in high dimensions and its upper critical dimension
- Universal aspects of curved, flat & stationary-state Kardar-Parisi-Zhang statistics
- Stationary State Skewness in Two Dimensional KPZ Type Growth
- The Kardar-Parisi-Zhang equation with spatially correlated noise: a unified picture from nonperturbative renormalization group
- Study of B --> pi l nu and B --> rho l nu decays and determination of |Vub|
- Directed d-mer diffusion describing Kardar-Parisi-Zhang type of surface growth
- Stochastic Model in the Kardar-Parisi-Zhang Universality With Minimal Finite Size Effects
- Skewness in (1+1)-dimensional Kardar-Parisi-Zhang-type growth
- Kurtosis of height fluctuations in dimensional KPZ Dynamics
- Numerical Method for Accessing the Universal Scaling Function for a Multi-Particle Discrete Time Asymmetric Exclusion Process