Abstract: For a probability-preserving ergodic dynamical system (X, T, μ) and an integrable
function f, the asymptotic almost sure behaviour of the ergodic sums S_N (f ) is described
by the Birkhoff Ergodic Theorem. The situation is much more complicated if f is not integrable,
a result by Aaronson forbids almost sure Limit Theorems. Instead, the notion of trimming is
introduced, by excluding the largest observations from SN . Trimmed limit Theorems are
well-studied for iids. In the dynamical setting, results are only known for systems exhibiting
strong mixing behaviour. We study trimming for irrational rotations in and functions with
polynomial singularities.
Trimmed ergodic sums for non-integrable functions over irrational rotations
12.12.2024 15:15 - 17:15
Organiser:
H. Bruin, R. Zweimüller
Location: