Orateur
Description
Networks appear naturally in a wide variety of context, including for example: biological networks , epidemics processes, electrical power grids and social networks. Most of those problems involve large dense graphs, that is graphs that have a large number of vertices and a number of edges that scales as the square of the number of vertices. Those graphs are too large to be represented entirely in the targeted applications. The idea is then to go from a combinatorial representation given by the graph to an infinite continuum representation: the graphons studied by Lovász and his co-authors. In this talk, I will present a joint work with Romain Abraham and Jean-François Delmas on probability-graphons, which are measure-valued graphons that generalises graphons to the case of weighted graphs and decorated graphs. I will explain how probability-graphons are used to define random weighted graph models, define a distance that control convergence for those sampled graphs, and give some topological results on this distance.
