## Electronic Journal of Probability

### Scaling limits for some random trees constructed inhomogeneously

#### Abstract

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

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

Dates
Accepted: 31 August 2017
First available in Project Euclid: 3 February 2018

https://projecteuclid.org/euclid.ejp/1517626965

Digital Object Identifier
doi:10.1214/17-EJP101

Mathematical Reviews number (MathSciNet)
MR3761565

Zentralblatt MATH identifier
06868350

#### Citation

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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