Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2003-05-06
Phys. Rev. E 68, 026103 (2003)
Physics
Condensed Matter
Statistical Mechanics
Revtex, 11 pages, 3 .eps figures included
Scientific paper
10.1103/PhysRevE.68.026103
We use the traveling front approach to derive exact asymptotic results for the statistics of the number of particles in a class of directed diffusion limited aggregation models on a Cayley tree. We point out that some aspects of these models are closely connected to two different problems in computer science, namely the digital search tree problem in data structures and the Lempel-Ziv algorithm for data compression. The statistics of the number of particles studied here is related to the statistics of height in digital search trees which, in turn, is related to the statistics of the length of the longest word formed by the Lempel-Ziv algorithm. Implications of our results to these computer science problems are pointed out.
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