Péter Frenkel: Convergence of graphs with intermediate density

Speaker: Péter Frenkel

Title: Convergence of graphs with intermediate density

Abstract: I will  define a  notion of graph convergence that interpolates between the Benjamini--Schramm convergence of bounded degree graphs and the dense graph convergence developed  by Laszlo Lovasz, Balazs Szegedy and others. A few examples of convergent sequences and a few results about estimable graph parameters will be given.

I will introduce tentative limit objects and prove that  any convergent sequence of large essential girth converges to a limit object.