Renewal theorems and mixing for non Markov flows with infinite measure

Ann. Inst. H. Poincaré (B) Probab. Statist. 56 (2020) 449-476.

Ian Melbourne and Dalia Terhesiu


Abstract We obtain results on mixing for a large class of (not necessarily Markov) infinite measure semiflows and flows. Erickson proved, amongst other things, a strong renewal theorem in the corresponding i.i.d. setting. Using operator renewal theory, we extend Erickson's methods to the deterministic (i.e. non-i.i.d.) continuous time setting and obtain results on mixing as a consequence.

Our results apply to intermittent semiflows and flows of Pomeau-Manneville type (both Markov and nonMarkov), and to semiflows and flows over Collet-Eckmann maps with nonintegrable roof function.


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