Maximal clades in random binary search trees

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• Svante Janson (Uppsala University)
• Thursday 26 February 2015, 14:30-15:30
• MR12.

If you have a question about this talk, please contact Andrew Thomason.

Define a clade in a binary tree as the set of external nodes that are descendants of the parent of some external node. (This has a biological background, but I am no expert on that.) If we consider only the internal nodes, a clade thus corresponds to a node with less than two children. Furthermore, a maximal clade corresponds to a node with less than two children, but with all ancestors having two children.

We study the number of maximal clades in a random binary search tree (or, equivalently, in a random phylogenetic tree with the Yule—Harding model). We use probabilistic methods to reprove and extend earlier results on moment asymptotics and asymptotic normality. In particular, we give an explanation of the curious phenomenon observed by Drmota, Fuchs and Lee (2014) that asymptotic normality holds, but one should normalize using half the variance.

This talk is part of the Combinatorics Seminar series.

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