Lovász László Miklós: Left and Right Convergence of Bounded Degree Graphs

Előadó: Lovász László Miklós

Cím: Left and Right Convergence of Bounded Degree Graphs

Absztrakt: There are several notions of convergence for sequences of bounded degree graphs. One such notion is left convergence (also known as local or Benjamini-Schramm convergence), which is based on counting neighborhood distributions. Another notion is right convergence, based on counting homomorphisms to a target (weighted) graph. We introduce some of these notions. Borgs, Chayes, Kahn and Lovász showed that a sequence of bounded degree graphs is left convergent if and only if it is right convergent for certain target graphs H with all weights (including loops) close to 1. We will give a short alternative proof of this statement.