Journal of Applied Probability
- J. Appl. Probab.
- Volume 50, Number 1 (2013), 228-238.
Asymptotic analysis of Hoppe trees
We introduce and analyze a random tree model associated to Hoppe's urn. The tree is built successively by adding nodes to the existing tree when starting with the single root node. In each step a node is added to the tree as a child of an existing node, where these parent nodes are chosen randomly with probabilities proportional to their weights. The root node has weight ϑ>0, a given fixed parameter, all other nodes have weight 1. This resembles the stochastic dynamic of Hoppe's urn. For ϑ=1, the resulting tree is the well-studied random recursive tree. We analyze the height, internal path length, and number of leaves of the Hoppe tree with n nodes as well as the depth of the last inserted node asymptotically as n→∞. Mainly expectations, variances, and asymptotic distributions of these parameters are derived.
J. Appl. Probab., Volume 50, Number 1 (2013), 228-238.
First available in Project Euclid: 20 March 2013
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Leckey, Kevin; Neininger, Ralph. Asymptotic analysis of Hoppe trees. J. Appl. Probab. 50 (2013), no. 1, 228--238. doi:10.1239/jap/1363784435. https://projecteuclid.org/euclid.jap/1363784435