Is the family of probabilities generated by a random walk on a finitely generated amenable group asymptotically invariant?

Is the family of probabilities μn (convolution) generated by a random walk μ on a finitely generated amenable group G asymptotically invariant (gμnμL10 for any gG)?

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

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

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