We prove that mixing on rank-one transformations is equivalent to "the uniform convergence of ergodic averages (as in the mean ergodic theorem) over subsequences of partial sums". In particular, all polynomial staircase transformations are mixing.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-1-4,
author = {Darren Creutz and Cesar E. Silva},
title = {Mixing on rank-one transformations},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {43-72},
zbl = {1230.37011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-1-4}
}
Darren Creutz; Cesar E. Silva. Mixing on rank-one transformations. Studia Mathematica, Tome 196 (2010) pp. 43-72. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-1-4/