Is the family of probabilities μn (convolution) generated by a random walk μ on a finitely generated amenable group G asymptotically invariant (‖gμn−μ‖L1→0 for any g∈G)?

I am not familiar with random walks on amenable groups. Please indicate reference on the subject.

**Answer**

**Attribution***Source : Link , Question Author : anom , Answer Author : Community*