Laszlo Toth: "Graph convergence, cost and the distortion function"

mercredi 7 nov. 2018, 14:00 → 15:00 Europe/Paris

435 (UMPA)

The notion of combinatorial cost for sequences of graphs was introduced by Elek as an analogue of the cost of measure preserving equivalence relations. We show that if a graph sequence is local-global convergent, then its combinatorial cost equals the cost of the limit graphing. We explore the analogous theory for p.m.p. actions of countable groups. 

We introduce the distortion function of p.m.p. actions as a secondary invariant related to the cost. It measures the complexity of generation near the cost. We compute the distortion function of actions of $\mathbb{Z}^d$, bound the distortion of lamplighters, and list some very basic, but still open questions regarding the distortion function.