Abstract: In a generalised preferential attachment tree, nodes arrive one at a time, and connect to existing nodes with probability proportional to a function of their degree, for some fixed function $f$. In such a process, a node is called a persistent hub if it becomes, and remains, the fixed node of maximal degree during the evolution of the process.
For a large class of generalised preferential attachment trees, we provide necessary and sufficient criteria for the emergence of a persistent hub, building on previous work by Dereich and Mörters; Galashin, and Banerjee and Bhamidi. In this talk, we explore some of the motivation behind this result, and some aspects of the proof.