Benjamini–Schramm limits of the Rauzy graphs

To a subshift over a finite alphabet, one can naturally associate an infinite family of finite graphs, called its Rauzy graphs. We will discuss the topological shape of these graphs (Benjamini–Schramm limit) under the certain combinatorial condition, and apply our result to different examples of dynamical origin, and exhibit the connections between the ergodic theory and the study of the graph structure based on geometric group theory. Our work generalizes and extends the ideas suggested by V. Kaimanovich and his master student for the Rauzy graphs associated with interval exchange transformations. The talk is based on the joint work with P.-H. Leemann, T. Nagnibeda and G. Veprev.