Quantitative weak mixing for interval exchange transformations

We establish a dichotomy for the rate of decay Cesàro averages correlations sufficiently regular functions typical interval exchange transformations (IET) which are not rigid rotations (for weak mixing had been previously established in works Katok–Stepin, Veech, and Avila–Forni). show that is either logarithmic or polynomial, according to whether IET rotation class (i.e., it can be obtained as induced map rotation) not. In latter case, we also spectral measures Lipschitz have local dimension bounded away from zero (by constant depending only on number intervals). our approach, upper bounds through estimates twisted Birkhoff sums functions, while lower based slow deviation ergodic govern relation between their maps.