Open Access
2018 Scaling limits for some random trees constructed inhomogeneously
Nathan Ross, Yuting Wen
Electron. J. Probab. 23: 1-35 (2018). DOI: 10.1214/17-EJP101


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 half real-line with a Poisson process having rate $(\ell +1)t^\ell dt$, for each positive integer $\ell $, and the growth of the combinatorial trees may be viewed as an inhomogeneous generalization of Rémy’s algorithm.


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Nathan Ross. Yuting Wen. "Scaling limits for some random trees constructed inhomogeneously." Electron. J. Probab. 23 1 - 35, 2018.


Received: 17 December 2016; Accepted: 31 August 2017; Published: 2018
First available in Project Euclid: 3 February 2018

zbMATH: 1390.60046
MathSciNet: MR3761565
Digital Object Identifier: 10.1214/17-EJP101

Primary: 05C10 , 60C05

Keywords: Continuum random tree , generalized Pólya urn , Gromov-Hausdorff-Prokhorov topology , line-breaking , Scaling limit

Vol.23 • 2018
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