Scaling limits for some random trees constructed inhomogeneously

2016/11/04 by Nathan Ross, Yuting Wen, Ross, Nathan +1
Mathematics · #05C10 #60C05 #Combinatorics (math.CO) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1611.01306

openalex publication_date 2016/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define some new sequences of recursively constructed random combinatorial trees, and show that, after properly rescaling graph distance and equipping the trees with the uniform measure on vertices, each sequence converges almost surely to a real tree in the Gromov-Hausdorff-Prokhorov sense. The limiting real trees are constructed via line-breaking the real half-line with a Poisson process having rate (ℓ+1)t^ℓ dt, for each positive integer ℓ, and the growth of the combinatorial trees may be viewed as an inhomogeneous generalization of Rémy's algorithm.

Citations

• The exploration process of inhomogeneous continuum random trees, and an extension of Jeulin’s local time identity
• The local weak limit of the minimum spanning tree of the complete graph

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