Appears in collection : 2022 - T2 - WS2 - Self-similarity of groups, trees and fractals

In my talk I will discuss an approach for randomness of groups and Schreier graphs. Two results in this direction will be formulated. Then I will describe a group construction based on the use of irreducible Schreier subshifts of finite type. Finally I will explain how subshifts can be used in group theory and try to explain how to gain a group of intermediate growth from the Thues-Morse sequence. Based on joint results with L.Bowen, R.Kravchenko, M.G.Benli, Y.Vorobets.