Erratum to: Operator renewal theory and mixing rates for dynamical systems with infinite measure

Abstract

We correct the statement and proof of Theorem 10.4 in our paper “Operator renewal theory and mixing rates for dynamical systems with infinite measure” [Inventiones Mathematicae 189 (2012) 61–110]. The main results in the paper are unaffected. In the original article, we developed a theory of operator renewal sequences in the context of infinite ergodic theory. For large classes of dynamical systems preserving an infinite measure, we determine the asymptotic behaviour of iterates Ln of the transfer operator, yielding results on mixing and rates of mixing. The main results, presented in Section 2 of the original article, focus on the restricted transfer operator 1Y L1Y where Y is a suitable finite measure subset of the full infinite measure system, and accordingly yield mixing results for observables supported on Y . Extensions to more general observables were described in specific cases in Section 1 based on results described in Sections 10 and 11.