# On ballistic deposition process on a strip

## TL;DR

This paper analyzes the combinatorial properties of the ballistic deposition model on a strip, providing limit theorems and moment calculations for the associated random tree structure.

## Contribution

It offers new probabilistic and combinatorial insights into the structure and behavior of the ballistic deposition process, extending previous models.

## Key findings

- Limit theorems for the number of roots
- Results on the average distance between roots
- Intricate moments calculations of the tree structure

## Abstract

We revisit the model of the ballistic deposition studied in \cite{bdeposition} and prove several combinatorial properties of the random tree structure formed by the underlying stochastic process. Our results include limit theorems for the number of roots and the empirical average of the distance between two successive roots of the underlying tree-like structure as well as certain intricate moments calculations.