Scaling limit of trees with vertices of fixed degrees and heights

Arthur Blanc-Renaudie; Emmanuel Kammerer

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arXiv · 2409.12897

Scaling limit of trees with vertices of fixed degrees and heights

Arthur Blanc-Renaudie·Emmanuel Kammerer

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Abstract

We consider large uniform random trees where we fix for each vertex its degree and height. We prove, under natural conditions of convergence for the profile, that those trees properly renormalized converge. To this end, we study the paths from random vertices to the root using coalescent processes. As an application, we obtain scaling limits of Bienaym\'e-Galton-Watson trees in varying environment.

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Arthur Blanc-Renaudie, Emmanuel Kammerer. 2024-09-19. Scaling limit of trees with vertices of fixed degrees and heights. https://arxiv.org/abs/2409.12897

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