Tied-down occupation times of infinite ergodic transformations

Aaronson, Jon; Sera, Toru

doi:10.48550/arxiv.1910.09846

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2023

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“…This was recently generalized in [16] to multi-ray settings by Sera and the fourth author, by using ideas from excursion theory. See also [2,3,15,18] and reference therein.…”

Section: Introductionmentioning

confidence: 99%

Arcsine law for random dynamics with a core

et al. 2023

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In their recent paper, Hata and Yano (2021 Stoch. Dyn. 2350006) first gave an example of random iterations of two piecewise linear interval maps without (deterministic) indifferent periodic points for which the arcsine law—a characterization of intermittent dynamics in infinite ergodic theory—holds. The key in the proof of the result is the existence of a Markov partition preserved by each interval maps. In the present paper, we give a class of random iterations of two interval maps without indifferent periodic points but satisfying the arcsine law, by introducing a concept of core random dynamics. As applications, we show that the generalized arcsine law holds for generalized Hata–Yano maps and piecewise linear versions of Gharaei–Homburg maps, both of which do not have a Markov partition in general.

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“…This was recently generalized in [16] to multi-ray settings by Sera and the fourth author, by using ideas from excursion theory. See also [2,3,15,18] and reference therein.…”

Section: Introductionmentioning

confidence: 99%