How a centred random walk on the affine group goes to infinity (Q1874506)

The author investigates so-called critical random walks on the affine group \(\mathbb{R}^+_*\times \mathbb{R}^d\) where the dilation parts of the random walk are centered. In particular, for left random walks the uniqueness of an invariant measure for the induced Markov chain on \(\mathbb{R}^d\) is derived. Moreover, it is shown that right random walks satisfying a moment condition tend to infinity.