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 → ∞, 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm198-2-3,
author = {Roland Zweim\"uller},
title = {Waiting for long excursions and close visits to neutral fixed points of null-recurrent ergodic maps},
journal = {Fundamenta Mathematicae},
volume = {201},
year = {2008},
pages = {125-138},
zbl = {1137.28004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm198-2-3}
}
Roland Zweimüller. Waiting for long excursions and close visits to neutral fixed points of null-recurrent ergodic maps. Fundamenta Mathematicae, Tome 201 (2008) pp. 125-138. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm198-2-3/