Application of the group algebra of the problem of the tail $\sigma$-algebra of a random walk on a group and the problem of ergodicity of a skew-product action

Two problems in measure theory are considered: that of the tail $C^*$- algebra of a random walk on a group, and that of ergodicity of a skew-product action. These problems are solved in a uniform way by using Banach algebras and harmonic analysis on a group.
Bibliography: 22 titles.