Recent progress on pointwise normality of self-similar measures
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915258546782208 |
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| author | Algom, Amir |
| author_facet | Algom, Amir |
| contents | 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 self-contained proof of a recent Theorem that the Rajchman property (decay of the Fourier transform) implies that typical elements in the support of the measure are normal to all bases; as no decay rate is required, this improves the classical criterion of Davenport, Erdos, and LeVeque (1964). Open problems regarding effective equidistribution, non-integer bases, and higher order correlations, are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18192 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Recent progress on pointwise normality of self-similar measures Algom, Amir Dynamical Systems Classical Analysis and ODEs Number Theory 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 self-contained proof of a recent Theorem that the Rajchman property (decay of the Fourier transform) implies that typical elements in the support of the measure are normal to all bases; as no decay rate is required, this improves the classical criterion of Davenport, Erdos, and LeVeque (1964). Open problems regarding effective equidistribution, non-integer bases, and higher order correlations, are discussed. |
| title | Recent progress on pointwise normality of self-similar measures |
| topic | Dynamical Systems Classical Analysis and ODEs Number Theory |
| url | https://arxiv.org/abs/2504.18192 |