Infinite measure renewal theorem and related results

TL;DR

This paper establishes abstract conditions for Krickeberg mixing in special flows with non-integrable roof functions, linking it to local central limit theorems, and verifies these for iid variables and Pomeau-Manneville maps.

Contribution

It introduces new abstract criteria for mixing in infinite measure flows and applies them to specific dynamical systems, expanding understanding of infinite ergodic theory.

Findings

Conditions for Krickeberg mixing established

Verification for iid renewal processes with infinite mean

Application to suspensions over Pomeau-Manneville maps

Abstract

We present abstract conditions under which a special flow over a probability preserving map with a non-integrable roof function is Krickeberg mixing. Our main condition is some version of the local central limit theorem for the underlying map. We check our assumptions for iid random variables (renewal theorem with infinite mean) and for suspensions over Pomeau-Manneville maps.