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The paper is devoted to generic translation flows corresponding to Abeliandifferentials on flat surfaces of arbitrary genus $g\ge 2$. These flows areweakly mixing by the Avila-Forni theorem. In genus 2, the H\"older property forthe spectral measures of these flows was established in our papers [10,12].Recently Forni [17], motivated by [10], obtained H\"older estimates forspectral measures in the case of surfaces of arbitrary genus. Here we combineForni's idea with the symbolic approach of [10] and prove H\"older regularityfor spectral measures of flows on random Markov compacta, in particular, fortranslation flows in all genera.

H\"older regularity for the spectrum of translation flows