Random forests and fermionic field theories
Kick-off event on Wed 29.10.25 at Institut Henri Poincaré. Inscriptions: link indico
The seminars at IHES will take place on the following Wednesdays: 12.11, 26.11 and 10.12, see program
Limiting Degree Distribution for a Sublinear Preferential Attachment Model with Communities
byCamille Cazaux
Abstract:For many real-world networks, such as the World Wide Web, the degree distribution follows a power law. It is therefore useful to have simple random graph models whose limiting degree distribution exhibits this same feature. With this motivation, physicists Albert-László Barabási and Réka Albert introduced the preferential attachment model that now bears their name. A further advantage of this model is that it incorporates temporal dynamics: starting from an initial graph \(\mathcal{G}_0\) the graph at time \(n+1\) is obtained from the graph at time \(n\), denoted \(\mathcal{G}_{n}\), by adding a new vertex \(v_{n+1}\). This vertex then attaches to one or several vertices of \(\mathcal{G}_n\) according to a preferential attachment rule, meaning that the probability of connecting to a given vertex of \(\mathcal{G}_n\) is proportional to its degree.
We present an extension of this model in which each vertex of the graph is assigned a community (or type), and in which the preferential attachment is sublinear; that is, the probability of attaching to a vertex \(u\) is proportional to \({\rm deg}(u)^\gamma\), where \(\gamma\) is a parameter taking values in \((0,1)\).
All talks Fall '25: random forests and fermionic field theories