Statistics of reduced words in locally free and braid groups: Abstract studies and application to ballistic growth model

TL;DR

This paper analyzes the average length of reduced words in locally free and braid groups, considering correlated and uncorrelated cases, and applies these findings to compute surface peaks in a ballistic growth model.

Contribution

It provides both numerical and analytical insights into how correlations affect reduced word lengths and applies these results to a ballistic growth surface model.

Findings

Correlation type influences average reduced word length

Analytical formulas for average number of surface peaks

Correlation can increase or decrease reduced word length

Abstract

We study numerically and analytically the average length of reduced (primitive) words in so-called locally free and braid groups. We consider the situations when the letters in the initial words are drawn either without or with correlations. In the latter case we show that the average length of the reduced word can be increased or lowered depending on the type of correlation. The ideas developed are used for analytical computation of the average number of peaks of the surface appearing in some specific ballistic growth model