Abstract
The aim of this chapter is to give a review of the author’s results on random walks on groups. In Section 2 we consider some useful properties of transition functions of random walks (see [7; part I]). Section 3 is devoted to a special decomposition of harmonic functions of random walks [8]. Finally, in Section 4 we deal with strong ratio limit theorems for random walks (see [7; part II] and [10]). Theorem 5 of Section 4 generalizes the well-known result by Avez [1] concerning symmetric random walks on discrete groups. Our list of references does not pretend to be complete.
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