Probabilistic limit of Rauzy graphs

Description

While the space of rooted gaphs admits a natural (metrizable) topology, this is not the case of the space of unrooted graphs. This problem can be overcome by turning a finite graph into a probability measure on the space of rooted graphs: simply choose the root uniformly at random. This simple but fruitful idea allows to define the Benjamini-Schramm convergence of a sequence of finite graphs as the weak-* limit of the associated probability measures. Any such limit is automatically a unimodular measure on the space of rooted graphs.
With my colleagues we computed the Benjamini-Schramm limit for Rauzy graphs associated to a subshift. For subshifts of finite type, the limit is the pushforward of the unique measure of maximal entropy. This measure is also characterised by its support $S$. More precisely, the limit of Rauzy graphs is the unique unimodular measure on $S$.

This is joint work with R. Grigorchuk, T. Nagnibeda, A. Skripchenko and G. Veprev

Period	4 Jun 2026
Held at	Taiwan University, Taiwan, Province of China