Electronic Journal of Probability

Scaling limits for some random trees constructed inhomogeneously

Nathan Ross and Yuting Wen

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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.

Article information

Electron. J. Probab., Volume 23 (2018), paper no. 5, 35 pp.

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

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Zentralblatt MATH identifier

Primary: 60C05: Combinatorial probability 05C10: Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25]

Scaling limit continuum random tree Gromov-Hausdorff-Prokhorov topology generalized Pólya urn line-breaking

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Ross, Nathan; Wen, Yuting. Scaling limits for some random trees constructed inhomogeneously. Electron. J. Probab. 23 (2018), paper no. 5, 35 pp. doi:10.1214/17-EJP101. https://projecteuclid.org/euclid.ejp/1517626965

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