Kurtosis of height fluctuations in $(1+1)$ dimensional KPZ Dynamics

Abstract

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 the connected diagrams leading to the value $Q=0.1523$ in the large-scale long-time limit.

12 pages, 2 figures, version accepted in J. Stat. Mech

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Cited by in corpus (6)

• The derivative of the Kardar-Parisi-Zhang equation is not in the KPZ universality class
• Gaussian statistics as an emergent symmetry of the stochastic Burgers equation
• A Renormalization Scheme and Skewness of Height Fluctuations in $(1+1)$-dimensional VLDS Dynamics
• Hyperskewness of $(1+1)$-dimensional KPZ Height Fluctuations
• Steady-state skewness and kurtosis from renormalized cumulants in $(2+1)$-dimensional stochastic surface growth
• Renormalized cumulants and velocity derivative skewness in Kolmogorov turbulence