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Universität Augsburg
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Universität Augsburg
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Dr. Bas Lodewijks
Universität Augsburg
spricht am
Mittwoch, 30. Juli 2025
um
14:00 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| We study a random tree model known as the Preferential Attachment tree with Vertex Death. Here, one can both add vertices to the tree as well as kill vertices. This model mimics the non-monotone growth of real-world networks, absent in classical preferential attachment models. One initialises the tree with a single root vertex labelled 1. At every step n, either a new vertex labelled n+1 is added to the tree and connected to an already present alive vertex selected preferentially according to a function b, or an already present vertex is selected preferentially according to a function d and killed. Killed vertices can make no new connections. We are interested in the behaviour of the richest alive vertex $I_n$ (with the largest degree) and the oldest alive vertex $O_n$ (with the smallest label). When $I_n$ converges almost surely, we say that a persistent hub exists. When $I_n$ does not converge but $I_n/O_n$ is tight, we say that persistence occurs, and when $I_n/O_n$ diverges to infinity we say lack of persistence occurs. We uncover three distinct regimes in which behaviour is different: (1) The infinite lifetime regime, where we provide conditions under which a persistent hub exists almost surely. (2) The rich are old regime, in which $O_n$ does not converge and where we provide conditions under which either persistence or lack of persistence occurs. (3) The rich die young regime, in which $O_n$ does not converge and where lack of persistence always occurs. We shall discuss how the three regimes can be identified and what drives the behaviour observed in each regime. Partly joint work with Markus Heydenreich. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Markus Heydenreich |