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On ballistic deposition process on a strip.

Toufik Mansour1, Reza Rastegar2, Alexander Roitershtein3

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Summary
This summary is machine-generated.

This study explores combinatorial properties of random trees generated by ballistic deposition. We establish limit theorems for root counts and root distances, enhancing understanding of this stochastic process.

Keywords:
05A1660F0560J10Primary 60K35Secondary 60C05ballistic depositiongenerating functionslimit theoremspacking modelsrandom sequential adsorptionrandom tree structures

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Area of Science:

  • Stochastic processes
  • Combinatorial probability
  • Random graph theory

Background:

  • Ballistic deposition is a fundamental model in statistical physics and materials science.
  • Understanding the emergent tree-like structures is crucial for various applications.
  • Previous work [5] established the basic model, leaving combinatorial properties unexplored.

Purpose of the Study:

  • To rigorously prove combinatorial properties of the random tree structure in ballistic deposition.
  • To derive limit theorems for key structural features.
  • To perform detailed moment calculations for the tree's properties.

Main Methods:

  • Combinatorial analysis of the stochastic process.
  • Application of limit theorems (e.g., laws of large numbers, central limit theorems).
  • Advanced probability calculations for moments.

Main Results:

  • Proof of combinatorial properties of the generated random trees.
  • Asymptotic results for the number of roots.
  • Limit theorems for the average distance between successive roots.
  • Precise calculations of intricate moments.

Conclusions:

  • The study provides a rigorous mathematical foundation for the combinatorial aspects of ballistic deposition.
  • The derived limit theorems offer insights into the large-scale structure of the random trees.
  • The moment calculations enable deeper quantitative analysis of the model's behavior.