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

TL;DR

This paper calculates the hyperskewness of height fluctuations in the (1+1)-dimensional KPZ equation, providing a precise value using a diagrammatic and renormalization approach, advancing understanding of surface growth statistics.

Contribution

It introduces a diagrammatic and renormalization method to compute the fifth cumulant of KPZ height fluctuations, a novel calculation for this stochastic growth model.

Findings

Hyperskewness value is 0.0835.

Method combines diagrammatic approach with renormalization.

Advances quantitative understanding of KPZ surface 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 $\widetilde{S} = 0.0835$.