Limit of trees with fixed degree sequence

2021/10/07 by Arthur Blanc-Renaudie, Blanc-Renaudie, Arthur
Agricultural and Biological Sciences · Mathematics · #60D05 60F05 #FOS: Mathematics #Mathematical Dynamics and Fractals #Plant nutrient uptake and metabolism #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2110.03378

openalex publication_date 2021/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show, under natural conditions, that uniform rooted trees with fixed degree sequence converge after renormalization toward inhomogeneous continuum random trees (ICRT). We also provide a sharp upper-bound for the tail of their heights. We also extend our results to P-trees, ICRT, and trees with random degree sequence. In passing we confirm a conjecture of Aldous, Miermont, and Pitman stating that Lévy trees are ICRT with random parameters.

Citations

• The exploration process of inhomogeneous continuum random trees, and an extension of Jeulin’s local time identity
• The Structure and Function of Complex Networks

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