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

TL;DR

This paper calculates the kurtosis of height fluctuations in 1+1 dimensional KPZ surface growth, providing a precise value using a diagrammatic renormalization approach for large-scale, long-time behavior.

Contribution

It introduces a diagrammatic renormalization method to evaluate the kurtosis of height fluctuations in the KPZ equation, yielding a specific quantitative result.

Findings

Kurtosis value Q=0.1523 in the large-scale limit

Diagrammatic renormalization effectively evaluates higher-order cumulants

Provides insights into the statistical properties of KPZ surface growth

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.