GraphConvStoch · Graph Convergence and Stochastic Processes on Graphs

The proposal covers the following interconnected topics:1. Benjamini-Schramm limits of finite graphs and stochastic processes on graphs;2. continuity and testability of graph parameters;3. factors of Bernoulli i.i.d. labellings;4. graph sequences from groups.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.