On the number of crossings in a random labelled tree with vertices in convex position

2019/02/14 by Octavio Arizmendi, Arizmendi, Octavio, Pilar Cano +3
Computer Science · Mathematics · #05C80 #Data Management and Algorithms #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1902.05223

openalex publication_date 2019/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the number of crossings in a random labelled tree with vertices in convex position is asymptotically Gaussian with mean n²/6 and variance n³/45. A similar result is proved for points in general position under mild constraints.

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