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SUMMARY:Limiting Degree Distribution for a Sublinear Preferential Attachme
 nt Model with Communities
DTSTART:20251126T104500Z
DTEND:20251126T114500Z
DTSTAMP:20260504T084600Z
UID:indico-event-15131@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Camille Cazaux (LPSM\, Sorbonne Université)\n\nSeed
  Seminar of Mathematics and Physics\nFall' 25: Random Forests and Fermioni
 c Field Theories \nFor 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 exhi
 bits this same feature. With this motivation\, physicists Albert-László 
 Barabási and Réka Albert introduced the preferential attachment model th
 at now bears their name. A further advantage of this model is that it inco
 rporates temporal dynamics: starting from an initial graph $\\mathcal{G}_0
 $\, the graph at time $n+1$ is obtained from the graph at time $n$\, denot
 ed $\\mathcal{G}_n$\, by adding a new vertex $v_{n+1}$. This vertex then a
 ttaches to one or several vertices of $\\mathcal{G}_n$ according to a pref
 erential attachment rule\, meaning that the probability of connecting to a
  given vertex of $\\mathcal{G}_n$ is proportional to its degree.\nWe prese
 nt an extension of this model in which each vertex of the graph is assigne
 d a community (or type)\, and in which the preferential attachment is subl
 inear\; that is\, the probability of attaching to a vertex $u$ is proporti
 onal to $\\deg(u)^\\gamma$\, where $\\gamma$ is a parameter taking values 
 in $(0\,1)$.\n========\nPour être informé des prochains séminaires vous
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 ssage vide.\n\nhttps://indico.math.cnrs.fr/event/15131/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/15131/
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