Convergence rates of limit theorems in random chord diagrams

J. E. Paguyo

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arXiv · 2104.01134

Convergence rates of limit theorems in random chord diagrams

J. E. Paguyo

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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.

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J. E. Paguyo. 2021-04-02. Convergence rates of limit theorems in random chord diagrams. https://arxiv.org/abs/2104.01134

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