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Journal of Statistical Physics

, Volume 177, Issue 4, pp 626–650 | Cite as

On Ballistic Deposition Process on a Strip

  • Toufik Mansour
  • Reza RastegarEmail author
  • Alexander Roitershtein
Article
  • 58 Downloads

Abstract

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.

Keywords

Ballistic deposition Packing models Random sequential adsorption Random tree structures Generating functions Limit theorems 

Mathematics Subject Classification

Primary 60K35 60J10 Secondary 60C05 05A16 60F05 

Notes

Acknowledgements

We are grateful to the referee for comments and feedback on the earlier version of the manuscript that resulted in a better presentation of results and proofs.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of HaifaHaifaIsrael
  2. 2.Occidental Petroleum CorporationHoustonUSA
  3. 3.Departments of Mathematics and Petroleum EngineeringUniversity of TulsaTulsaUSA
  4. 4.Department of StatisticsTexas A&M UniversityCollege StationUSA

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