For random Young towers with ergodic driving, self-normalized Birkhoff sums converge to a standard Brownian motion in Wasserstein distance at rate O(n^{-1/4+1/(2q)}).
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Quenched invariance principle with a rate for random dynamical systems
For random Young towers with ergodic driving, self-normalized Birkhoff sums converge to a standard Brownian motion in Wasserstein distance at rate O(n^{-1/4+1/(2q)}).