  Motivated by work of Dolgopyat and N\'andori, we establish a general method
for upgrading limit theorems for Birkhoff sums and cocycles over dynamical
systems to mixing limit theorems under mild ergodicity and hyperbolicity
assumptions. Building on previous work of Al-Saqban and Forni, we apply this
method to obtain mixing limit theorems for particular subbundles of the
Kontsevich-Zorich cocycle. In forthcoming work of Arana-Herrera and Honaryar
these results are applied to study the arithmetic/homological complexity of
long simple closed geodesics on negatively curved surfaces.
