Random walks on compact semigroups
Arunava Mukherjea, T. C. Sun, Nicolas A. Tserpes · Proceedings of the American Mathematical Society · 1973
Let β \beta be a regular Borel probability measure with support F F on a compact semigroup S S . Let X 1 , X 2 , ⋯ {X_1},{X_2}, \cdots be a sequence of independent random variables on some probability space ( Ω , Σ , P ) (\Omega ,\Sigma ,P) with values in S S , having identical distribution P ( X n ∈ B ) = β ( B ) P({X_n} \in B) = \beta (B) . The random walk Z n = X 1 X 2 ⋯ X n {Z_n} = {X_1}{X_2} \cdots {X_n} is studied in this paper. Let D D be the closed semigroup generated by F F . An element x x in