We revisit the model of the ballistic deposition studied in Atar et al. (Electron Commun Probab 6:31–38, 2001) 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.
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- Ballistic deposition
- Generating functions
- Limit theorems
- Packing models
- Random sequential adsorption
- Random tree structures
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics