Drift of random walks on abelian covers of finite volume homogeneous spaces
Drift of random walks on abelian covers of finite volume homogeneous spaces
Let $G$ be a connected simple real Lie group, $\Lambda_{0}\subseteq G$ a lattice and $\Lambda \unlhd \Lambda_{0}$ a normal subgroup such that $\Lambda_{0}/\Lambda\simeq \mathbb{Z}^d$. We study the drift of a random walk on the $\mathbb{Z}^d$-cover $\Lambda\backslash G$ of the finite volume homogeneous space $\Lambda_{0}\backslash G$. This walk is defined by …