Convergence rate for the number of crossings in a random labelled tree

Santiago Arenas-Velilla and Octavio Arizmendi

Statistics & Probability Letters, 2023, vol. 203, issue C

Abstract: We consider the number of crossings in a random labelled tree with vertices in convex position. We give a new proof of the fact that this quantity is asymptotically Gaussian with mean n2/6 and variance n3/45. Furthermore, we give an estimate for the Kolmogorov distance to a Gaussian distribution which implies a convergence rate of order n−1/2.

Keywords: Crossings; Random labelled trees; Normal approximation (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spl.2023.109916

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