Persistence and survival in equilibrium step fluctuations

TL;DR

This paper reviews analytic, numerical, and experimental studies on the first-passage properties of equilibrium step fluctuations on vicinal surfaces, highlighting the effects of various physical and measurement factors.

Contribution

It provides a comprehensive analysis of persistence and survival probabilities in step fluctuations, integrating experimental data with theoretical models and discussing measurement effects.

Findings

Experimental results align with theoretical predictions for step fluctuation models.

Finite sampling and system size significantly influence observed first-passage properties.

Different microscopic mass transport mechanisms affect fluctuation behaviors.

Abstract

Results of analytic and numerical investigations of first-passage properties of equilibrium fluctuations of monatomic steps on a vicinal surface are reviewed. Both temporal and spatial persistence and survival probabilities, as well as the probability of persistent large deviations are considered. Results of experiments in which dynamical scanning tunneling microscopy is used to evaluate these first-passage properties for steps with different microscopic mechanisms of mass transport are also presented and interpreted in terms of theoretical predictions for appropriate models. Effects of discrete sampling, finite system size and finite observation time, which are important in understanding the results of experiments and simulations, are discussed.