Universal aspects of curved, flat & stationary-state Kardar-Parisi-Zhang statistics

Abstract

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 (Phys. Rev. Lett. {\bf 110}, 210604 (2013)), we establish here the universality of these phenomena, examining scaling behaviors of directed polymers in a random medium, the stochastic heat equation with multiplicative noise, and kinetically roughened KPZ growth models. We emphasize the value of cross KPZ-Class universalities, revealing crossover effects of experimental relevance. Finally, we illustrate the great utility of KPZ scaling theory by an optimized numerical analysis of the Ulam problem of random permutations.

5 pages, 3 figures, 1 table

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• An appetizer to modern developments on the Kardar-Parisi-Zhang universality class
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• Dynamical phase transition in large deviation statistics of the Kardar-Parisi-Zhang equation
• Large deviations of surface height in the $1+1$-dimensional Kardar-Parisi-Zhang equation: exact long-time results for $\lambda H<0$
• Electrodynamic duality and vortex unbinding in driven-dissipative condensates
• Universality of fluctuations in the Kardar-Parisi-Zhang class in high dimensions and its upper critical dimension
• Short-time height distribution in 1d KPZ equation: starting from a parabola
• Finite-time fluctuations for the totally asymmetric exclusion process
• Kardar-Parisi-Zhang universality in the phase distributions of one-dimensional exciton-polaritons
• Height distribution tails in the Kardar-Parisi-Zhang equation with Brownian initial conditions
• Interface fluctuations for deposition on enlarging flat substrates
• Searching for the Tracy-Widom distribution in nonequilibrium processes
• Diffusion in time-dependent random media and the Kardar-Parisi-Zhang equation
• Optimal paths of non-equilibrium stochastic fields: the Kardar-Parisi-Zhang interface as a test case
• Half-space stationary Kardar-Parisi-Zhang equation
• The one-dimensional Kardar-Parisi-Zhang and Kuramoto-Sivashinsky universality class: limit distributions
• Spherical model of growing interfaces
• Tail of the two-time height distribution for KPZ growth in one dimension
• Geometry dependence in linear interface growth
• Kardar-Parisi-Zhang growth on one-dimensional decreasing substrates
• Dynamical universality classes of simple growth and lattice gas models
• Probability distributions for directed polymers in random media with correlated noise
• Circular Kardar-Parisi-Zhang interfaces evolving out of the plane
• $1/f^{\alpha }$ power spectrum in the Kardar-Parisi-Zhang universality class
• Free energy distribution of the stationary O'Connell-Yor directed random polymer model
• Scaling of local roughness distributions
• KPZ universality class and the anchored Toom interface
• Kinetic roughening of the urban skyline
• Width and extremal height distributions of fluctuating interfaces with window boundary conditions
• Height fluctuations in homoepitaxial thin film growth: A numerical study
• KPZ fluctuations in finite volume
• Exactly solvable models of growing interfaces and lattice gases: the Arcetri models, ageing and logarithmic sub-ageing
• Kurtosis of height fluctuations in $(1+1)$ dimensional KPZ Dynamics
• 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
• Hyperskewness of $(1+1)$-dimensional KPZ Height Fluctuations
• One-point height fluctuations and two-point correlators of $(2+1)$ cylindrical KPZ systems
• Steady-state skewness and kurtosis from renormalized cumulants in $(2+1)$-dimensional stochastic surface growth
• Height distributions in interface growth: The role of the averaging process