Universal fluctuations in radial growth models belonging to the KPZ universality class

Abstract

We investigate the radius distributions (RD) of surfaces obtained with large-scale simulations of radial clusters that belong to the KPZ universality class. For all investigated models, the RDs are given by the Tracy-Widom distribution of the Gaussian unitary ensemble, in agreement with the conjecture of the KPZ universality class for curved surfaces. The quantitative agreement was also confirmed by two-point correlation functions asymptotically given by the covariance of the Airy${}_2$ process. Our simulation results fill the last lacking gap of the conjecture that had been recently verified analytically and experimentally.

5 pages, 5 figures

References in corpus (8)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• The one-dimensional KPZ equation: an exact solution and its universality
• Universal Fluctuations of Growing Interfaces: Evidence in Turbulent Liquid Crystals
• Growing interfaces uncover universal fluctuations behind scale invariance
• Finite time corrections in KPZ growth models
• The height distribution of the KPZ equation with sharp wedge initial condition: numerical evaluations
• Finite-size effects in roughness distribution scaling
• Maximal and minimal height distributions of fluctuating interfaces

Cited by in corpus (40)

• A KPZ Cocktail- Shaken, not stirred: Toasting 30 years of kinetically roughened surfaces
• The one-dimensional KPZ equation and its universality class
• Dynamic Correlators of Fermi-Pasta-Ulam Chains and Nonlinear Fluctuating Hydrodynamics
• Universal fluctuations in the growth of semiconductor thin films
• Universal correlators and distributions as experimental signatures of 2+1 Kardar-Parisi-Zhang growth
• Kardar-Parisi-Zhang universality class in 2+1 dimensions: Universal geometry-dependent distributions and finite-time corrections
• Quantum Loewner Evolution
• Universal aspects of curved, flat & stationary-state Kardar-Parisi-Zhang statistics
• Statistics of circular interface fluctuations in an off-lattice Eden model
• Coupled Kardar-Parisi-Zhang Equations in One Dimension
• Universal fluctuations in KPZ growth on one-dimensional flat substrates
• Non-universal parameters, corrections and universality in Kardar-Parisi-Zhang growth
• Interface fluctuations for deposition on enlarging flat substrates
• Initial pseudo-steady state & asymptotic KPZ universality in semiconductor on polymer deposition
• Searching for the Tracy-Widom distribution in nonequilibrium processes
• On the origins of scaling corrections in ballistic growth models
• Topology and the Kardar-Parisi-Zhang universality class
• Random geometry and the Kardar-Parisi-Zhang universality class
• Non-universality of front fluctuations for compact colonies of non-motile bacteria
• Kardar-Parisi-Zhang growth on one-dimensional decreasing substrates
• Geometry dependence in linear interface growth
• Eden model with nonlocal growth rules and the kinetic roughening in biological systems
• The circular Kardar-Parisi-Zhang equation as an inflating, self-avoiding ring polymer
• Circular Kardar-Parisi-Zhang interfaces evolving out of the plane
• Nonequilibrium criticality driven by Kardar-Parisi-Zhang fluctuations in the synchronization of oscillator lattices
• Kardar-Parisi-Zhang universality class for the critical dynamics of reaction-diffusion fronts
• Dimensional fragility of the Kardar-Parisi-Zhang universality class
• Eden clusters in three-dimensions and the Kardar-Parisi-Zhang universality class
• Hallmarks of the Kardar-Parisi-Zhang universality class elicited by scanning probe microscopy
• Spreading fronts of wetting liquid droplets: microscopic simulations and universal fluctuations
• Growth and form of melanoma cell colonies
• Width and extremal height distributions of fluctuating interfaces with window boundary conditions
• Height distributions in competitive one-dimensional Kardar-Parisi-Zhang systems
• Height fluctuations in homoepitaxial thin film growth: A numerical study
• KPZ fluctuations in finite volume
• Radial Restricted Solid-on-Solid and Etching Interface Growth Models
• Surface growth on treelike lattices and the upper critical dimension of the KPZ class
• Kardar-Parisi-Zhang growth on square domains that enlarge nonlinearly in time
• One-point height fluctuations and two-point correlators of $(2+1)$ cylindrical KPZ systems
• Height distributions in interface growth: The role of the averaging process