An ergodic theorem for the quasi-regular representation of the free group
Résumé
We prove the weak-* convergence of a certain sequence of averages of unitary operators associated to the action of the free group on its Gromov boundary. This result, which can be thought as an ergodic theorem a la von Neumann with coefficients, provides a new proof of the irreducibility of the quasi-regular representation of the free group.