Leírás
Előadó: Konrad Krolicki
Cím: Limits of weighted graphs
Absztrakt: The talk will cover parts of my PhD thesis. The aim is to extend to idea of the Benjamini-Schramm convergence of graphs to graphs with weighted vertices. In order to do that, we introduce the space of rooted cocycles (which correspond to weighted graphs) and we consider a special class measures on that space, which we call the Quasi-Invariant Random Cocycles. These serve the same function as the Invariant Random Subgroups for graphs. Furthermore, we consider hyperfiniteness in the weighted setting and we will try to show the progress we made on obtaining a weighted version of Schramm's theorem: that a limit of a convergent sequence of cocycles is hyperfinite if and only if the sequence is hyperfinite. Joint work with Gabor Elek.