Abstract: After Birkhoff’s pointwise ergodic theorem was proved in 1931, there have been many attempts to generalize the theorem along any random sequence instead of taking the entire sequence (n). In this talk, we will review some known results along this line and present a condition under which the ergodic averages oscillate in an extremely possible way. This talk is based on the joint work with Madhumita Roy and Máté Wierdl.
