Convergence rates of limit theorems in random chord diagrams
Probability
2023-01-13 v2 Combinatorics
Abstract
We study the asymptotic distributions of the number of crossings and the number of simple chords in a random chord diagram. Using size-bias coupling and Stein's method, we obtain bounds on the Kolmogorov distance between the distribution of the number of crossings and a standard normal random variable, and on the total variation distance between the distribution of the number of simple chords and a Poisson random variable. As an application, we provide explicit error bounds on the number of chord diagrams containing no simple chords.
Keywords
Cite
@article{arxiv.2104.01134,
title = {Convergence rates of limit theorems in random chord diagrams},
author = {J. E. Paguyo},
journal= {arXiv preprint arXiv:2104.01134},
year = {2023}
}
Comments
12 pages, 1 figure. Strengthened main theorem to the Kolmogorov distance. Added a new section. Made some additional minor revisions