Graph Convergence and Stochastic Processes on Graphs

Marie Curie Fellowship PIEF-GA-2013-629958 - GraphConvStoch, Adam Timar

The project started on May 01, 2015.

The project covers the following interconnected topics: The central object for the proposed research is sequences of sparse graphs (either coming from some random graph model or from Cayley graphs) and their Benjamini-Schramm limits. Convergence of optimal values of graph parameters (and the stochastic processes that lie behind them) are to be studied. A typical question is how the limit is related to the optimal value arising as a factor of i.i.d.. The context of such questions is not only general convergent graph sequences and sequences of random regular graphs but also other models (e.g. scale-free graph families). Finally, questions on the asymptotic properties of balls in Cayley graphs are to be addressed.