Hyperskewness of $(1+1)$-dimensional KPZ Height Fluctuations

Abstract

We evaluate the fifth order normalized cumulant, known as hyperskewness, of height fluctuations dictated by the $(1+1)$-dimensional KPZ equation for the stochastic growth of a surface on a flat geometry in the stationary state. We follow a diagrammatic approach and invoke a renormalization scheme to calculate the fifth cumulant given by a connected loop diagram. This, together with the result for the second cumulant, leads to the hyperskewness value $\tilde{S}=0.0835$.

11 pages, 2 figures, version accepted for publication in J. Stat. Mech.: Theory and Exp

References in corpus (3)

• Growing interfaces uncover universal fluctuations behind scale invariance
• An exact solution for the KPZ equation with flat initial conditions
• Skewness in (1+1)-dimensional Kardar-Parisi-Zhang-type growth

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