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math.DS2025
Recent progress on pointwise normality of self-similar measures
Amir Algom
This article is an exposition of recent results and methods on the prevalence of normal numbers in the support of self-similar measures on the line. We also provide an essentially…
math.DS2025
Spectral gaps and Fourier decay for self-conformal measures in the plane
Amir Algom, Federico Rodriguez Hertz, Zhiren Wang
Let be a self-conformal IFS on the plane, satisfying some mild non-linearity and irreducibility conditions. We prove a uniform spectral gap estimate for the…