2 problems

Let $(\Gamma,\tau)$ be a measured group, and let its Poisson boundary be $(B,\nu)$. For $p\in[1,\infty)$, the associated representation is … for $\gamma\in\Gamma$ and…

Let $\mathcal{T}$ be an oriented tree with a fixed end, and let $(Z_n)$ be a random walk with bounded range on $\mathbb{Z}_2\wr\mathcal{T}$. Write $(X_n)$ for its projection to…