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Tejas Iyer: Persistent hubs in generalised preferential attachment trees.

Time: Wed 2024-05-22 15.15 - 16.00

Location: Cramér room, campus Albano, house 1, floor 3

Participating: Tejas Iyer (WIAS Berlin)

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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.