We show that all rank-one transformations are subsequence boundedly rationally ergodic and that there exist rank-one transformations that are not weakly rationally ergodic.
@article{arxiv.1310.5084,
title = {Subsequence Rational Ergodicity of Rank-One Transformations},
author = {Francisc Bozgan and Anthony Sanchez and Cesar E. Silva and David Stevens and Jane Wang},
journal= {arXiv preprint arXiv:1310.5084},
year = {2014}
}