8 papers
Structure of 2-step nilpotent ergodic averages for distinct-degree polynomials
Andreas Koutsogiannis, Borys Kuca, Wenbo Sun
We investigate manifestations of the Nilpotent Heuristic, which posits that recurrence and convergence phenomena known for measure-preserving -systems extend to nilpo…
Joint ergodicity - 40 years on
Borys Kuca
Recent years have seen dramatic progress in the study of joint ergodicity, i.e. a scenario in which a multiple ergodic average converges in norm to the product of integrals of indi…
Quantitative concatenation for polynomial box norms
Noah Kravitz, Borys Kuca, James Leng
Using PET and quantitative concatenation techniques, we establish box-norm control with the "expected" directions for counting operators for general multidimensional polynomial pro…
Seminorm control for ergodic averages with commuting transformations and pairwise dependent polynomial iterates
Nikos Frantzikinakis, Borys Kuca
We examine multiple ergodic averages of commuting transformations with polynomial iterates in which the polynomials may be pairwise dependent. In particular, we show that such aver…
Seminorm estimates and joint ergodicity for pairwise independent Hardy sequences
Sebastián Donoso, Andreas Koutsogiannis, Borys Kuca +2
We develop a robust structure theory for multiple ergodic averages of commuting transformations along Hardy sequences of polynomial growth. We then apply it to derive a number of n…
Ergodic averages for sparse corners
Nikos Frantzikinakis, Borys Kuca
We develop a framework for the study of the limiting behavior of multiple ergodic averages with commuting transformations when all iterates are given by the same sparse sequence; t…