We want to identify the Poisson boundary (i.e. the tail algebra of the path space) of random walks in groups with
certain hyperbolic properties such as Baumslag type groups or the lamplighter group, among others.
We further want to generalise the entropy approach to random walks whose increments obey certain dependencies
(e.g. Gibbs) and establish a relationship between geometric boundaries of the group and the tail algebra of such a
random walk.