Electronic Journal of Probability
- Electron. J. Probab.
- Volume 23 (2018), paper no. 5, 35 pp.
Scaling limits for some random trees constructed inhomogeneously
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.
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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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