Action convergence of graphs, matrices and operators

The notion of action convergence is motivated by problems in graph limit theory and by applications for random matrices and random graphs. In general, the main goal of graph limit theory is to define useful similarity metrics on graphs, and to find limit objects of convergent sequences. This approach makes it possible to use various tools from analysis and probability theory to solve problems in combinatorics. In the current work, we extended some of the already existing convergence notions for a more general setup, for example, for matrices with both positive and negative entries. The limit objects turned out to be bounded operators on certain L^2 spaces in this case. This convergence notion and possible applications will be presented in the talk.

Joint work with Balázs Szegedy.