Temporal Regularity for Random Walk on Discrete Nilpotent Groups

It is shown that for any symmetric, finitely supported probability measure μ on a finitely generated discrete virtually nilpotent group, the difference between the convolution powers μⁿ and μⁿ⁺¹ is O(n⁻¹) in L¹ norm, as n → ∞. A generalization concerning random walk on certain graphs is also given.