Abstract

We introduce a new class of sparse sequences that are ergodic and pointwise universally (Formula presented.) -good for ergodic averages; that is, sequences along which the ergodic averages converge almost surely to the projection to invariant functions. These sequences are generated randomly as return or hitting times in systems exhibiting a rapid correlation decay. This can be seen as a natural variant of Bourgain's return times theorem. For example, we obtain that for any (Formula presented.), the sequence (Formula presented.) is ergodic and pointwise universally (Formula presented.) -good for Lebesgue almost every (Formula presented.). Our approach builds on techniques developed by Frantzikinakis, Lesigne and Wierdl in their study of sequences generated by independent random variables, which we adapt to the non-independent case. © 2025 The Author(s). Bulletin of the London Mathematical Society is copyright © London Mathematical Society.