Tied-down occupation times of infinite ergodic transformations

Jon Aaronson*, Toru Sera

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We prove distributional limit theorems (conditional and integrated) for the occupation times of certain weakly mixing, pointwise dual ergodic transformations at “tied-down” times immediately after “excursions”. The limiting random variables include the local times of q-stable Lévy-bridges (1 < q ≤ 2) and the transformations involved exhibit “tied-down renewal mixing” properties which refine rational weak mixing. Periodic local limit theorems for Gibbs—Markov and AFU maps are also established.

Original languageEnglish
Pages (from-to)3-47
Number of pages45
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - Dec 2022


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