Random walks on Baumslag-Solitar groups

We consider random walks on non-amenable Baumslag–Solitar groups BS(p, q) and describe their Poisson–Furstenberg boundary. The latter is a probabilistic model for the long-time behaviour of the random walk. In our situation, we identify it in terms of the space of ends of the Bass–Serre tree and the real line using Kaimanovich’s strip criterion.