Stationary actions of locally compact groups are conservative and never of type I or II_infty; under Lp-density conditions they admit a universal compact Radon-Nikodym model, but a random walk on the real affine group yields a Poisson boundary with no continuous model.
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On stationary actions of locally compact groups and their Radon-Nikodym cocycles
Stationary actions of locally compact groups are conservative and never of type I or II_infty; under Lp-density conditions they admit a universal compact Radon-Nikodym model, but a random walk on the real affine group yields a Poisson boundary with no continuous model.