Self-similar measures pushed to non-degenerate curves satisfy optimal L^p-flattening estimates for their Fourier transforms, implying quantitative dimension improvement under convolution.
H\"older regularity of stationary measures
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abstract
We consider smooth random dynamical systems defined by a distribution with a finite moment of the norm of the differential, and prove that under suitable non-degeneracy conditions any stationary measure must be H\"older continuous. The result is a vast generalization of the classical statement on H\"older continuity of stationary measures of random walks on linear groups.
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2025 1verdicts
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$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves
Self-similar measures pushed to non-degenerate curves satisfy optimal L^p-flattening estimates for their Fourier transforms, implying quantitative dimension improvement under convolution.