Q Seminar: Meltem Ünel

Speaker: Meltem Ünel

Title: Height-biased trees: some new results 

Abstract: Given $\mu \in \mathbb{R}$, a height-biased tree of size $n$ is a random planar tree $T_n$ with $n$ vertices whose distribution is given by $P(T_n = t ) \propto e^{−\mu h(t)} $, where $t$ is a fixed tree with $n$ vertices, and $h(t)$ is the height of $t$.

The case where $\mu$ is a fixed real constant has been studied by Durhuus and Unel and became part of the speaker’s PhD thesis. In this talk, we will present some statistics of height-biased trees when $\mu=\mu(n)$ is a sequence with positive terms depending on $n$: in particular, its height and its width, which turn out to differ from the uniform case.

The talk is based on arXiv:2512.17747, co-authored with L. Addario-Berry, B. Corsini, and N. Maitra.