Al-Khwarizmi
Applied Mathematics Webinar 

Next talk : September 09, 2026. 

Wednesday - 2:00 pm (GMT) 

Zoom link: https://ksu-hub.zoom.us/j/97753107489

Speaker: Tiffany Y. Y. Lo, Stockholm University, Sweden. 

Title: The number of descendants in a preferential attachment graph.

Abstract: We study the number $X^{(n)}$ of vertices that can be reached from the last added vertex $n$ via a directed path (the descendants) in the standard preferential attachment random graph. In this model, vertices are sequentially added, each born with out-degree $m> 2$; the endpoint of each outgoing edge is chosen among previously added vertices with probability proportional to the current degree of the vertex plus some number $\rho$. We show that $X^{(n)}/n^\nu$ converges in distribution as $n\to\infty$, where $\nu$ depends on both $m$ and $\rho$, and the limiting distribution is given by a product of a constant factor and the $(1-\nu)$-th power of a Gamma(m/(m − 1), 1) variable. I will discuss the main result and some aspects of the proof. 

Joint work with Svante Janson.