Level Crossing Analysis of Growing surfaces

TL;DR

This paper analyzes the frequency of positive slope crossings in surface growth models, providing exact results for the random deposition model and the KPZ equation before singularities form.

Contribution

It offers the first exact level crossing analysis for the random deposition model and the KPZ equation in the strong coupling limit prior to singularity formation.

Findings

Exact level crossing frequency for the random deposition model.

Exact level crossing frequency for the KPZ equation in strong coupling.

Insights into surface growth dynamics before singularities occur.

Abstract

We investigate the average frequency of positive slope $\nu_{\alpha}^{+} $, crossing the height $\alpha = h- \bar h$ in the surface growing processes. The exact level crossing analysis of the random deposition model and the Kardar-Parisi-Zhang equation in the strong coupling limit before creation of singularities are given.