Waiting for long excursions and close visits to neutral fixed points of null-recurrent ergodic maps
Volume 198 / 2008
Fundamenta Mathematicae 198 (2008), 125-138
MSC: Primary 28D05, 37A40, 37C30.
DOI: 10.4064/fm198-2-3
Abstract
We determine, for certain ergodic infinite measure preserving transformations $T$, the asymptotic behaviour of the distribution of the waiting time for an excursion (from some fixed reference set of finite measure) of length larger than $l$ as $l\rightarrow \infty $, generalizing a renewal-theoretic result of Lamperti. This abstract distributional limit theorem applies to certain weakly expanding interval maps, where it clarifies the distributional behaviour of hitting times of shrinking neighbourhoods of neutral fixed points.
