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arXiv · 2110.03378

Limit of trees with fixed degree sequence

Arthur Blanc-Renaudie
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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 L\'evy trees are ICRT with random parameters.

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Arthur Blanc-Renaudie. 2021-10-07. Limit of trees with fixed degree sequence. https://arxiv.org/abs/2110.03378

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