Trimmed Ergodic Sums for Non-integrable Functions over Irrational Rotations
Vortrag von Max Auer
Sprecher eingeladen von: Prof. Dr. Corinna Ulcigrai
Datum: 05.12.24 Zeit: 11.00 - 12.00 Raum: Y34K01
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 S_N(f) . 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.