The Necklace Process: A Generating Function Approach
Probability
2018-07-25 v2 Combinatorics
Abstract
The "necklace process", a procedure constructing necklaces of black and white beads by randomly choosing positions to insert new beads (whose color is uniquely determined based on the chosen location), is revisited. This article illustrates how, after deriving the corresponding bivariate probability generating function, the characterization of the asymptotic limiting distribution of the number of beads of a given color follows as a straightforward consequence within the analytic combinatorics framework.
Cite
@article{arxiv.1801.09934,
title = {The Necklace Process: A Generating Function Approach},
author = {Benjamin Hackl and Helmut Prodinger},
journal= {arXiv preprint arXiv:1801.09934},
year = {2018}
}