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Traveling front solutions to directed diffusion-limited aggregation, digital search trees, and the Lempel-Ziv data
1Laboratoire de Physique Théorique (FER 2603 du CNRS), Université Paul Sabatier, 31062 Toulouse Cedex, France.
Summary
This study analyzes particle number statistics in diffusion-limited aggregation models on Cayley trees. Results offer insights into digital search trees and Lempel-Ziv data compression algorithms.
Area of Science:
- Mathematical Physics
- Complex Systems
Background:
- Directed diffusion-limited aggregation (DLA) models exhibit complex growth patterns.
- Cayley trees provide a fundamental structure for studying branching processes.
- Connections between DLA and computer science algorithms are increasingly recognized.
Purpose of the Study:
- Derive exact asymptotic results for particle number statistics in DLA on Cayley trees.
- Explore the relationship between DLA models and problems in computer science.
- Provide implications for digital search trees and Lempel-Ziv data compression.
Main Methods:
- Utilized the traveling front approach for analysis.
- Derived exact asymptotic results for particle statistics.
- Established connections to computational problems.
Main Results:
- Obtained precise statistical properties of particle numbers in the studied DLA models.
- Demonstrated a direct link between DLA particle statistics and digital search tree height.
- Showed a relationship to the length of the longest word in Lempel-Ziv compression.
Conclusions:
- The traveling front method yields exact results for DLA on Cayley trees.
- DLA models offer a framework for understanding data structures and compression algorithms.
- Results have direct implications for analyzing the efficiency of digital search trees and Lempel-Ziv.