Holder regularity for the spectrum of translation flows

The paper is devoted to generic translation flows corresponding to Abelian differentials on flat surfaces of arbitrary genus $gge 2$. These flows are weakly mixing by the Avila-Forni theorem. In genus 2, the Holder property for the spectral measures of these flows was established in our papers [10,12]. Recently Forni [17], motivated by [10], obtained Holder estimates for spectral measures in the case of surfaces of arbitrary genus. Here we combine Fornis idea with the symbolic approach of [10] and prove Holder regularity for spectral measures of flows on random Markov compacta, in particular, for translation flows in all genera.