  This note contains old instead of new results about random walks on groups,
which may serve as a small supplement to the author's monograph ``Random Walks
on Infinite Graphs and Groups'' (Cambridge Univ. Press 2000/2009). First, we
exhibit a basic exercise on the periodicity classes of random walk. The second
topic concerns some basics on ratio limits for random walks, which had been
published ``only'' in German in the 1970ies.

Probability