Weaker quantization dimension results for self-similar measures
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908797537091584 |
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| author | Verma, Saurabh Dubey, Shivam |
| author_facet | Verma, Saurabh Dubey, Shivam |
| contents | In this paper, we investigate the quantization dimension of self-similar measures, particularly when the IFS does not satisfy the separation condition, but the sub-IFS at some level satisfies the separation condition. Further, we study the approximation of the space of Borel probability measures $\mathcal{P}(\mathbb{R}^m)$ with respect to the geometric mean error, i.e., the quantization dimension of order zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20531 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weaker quantization dimension results for self-similar measures Verma, Saurabh Dubey, Shivam Dynamical Systems Probability Primary 28A80, Secondary 28A78 In this paper, we investigate the quantization dimension of self-similar measures, particularly when the IFS does not satisfy the separation condition, but the sub-IFS at some level satisfies the separation condition. Further, we study the approximation of the space of Borel probability measures $\mathcal{P}(\mathbb{R}^m)$ with respect to the geometric mean error, i.e., the quantization dimension of order zero. |
| title | Weaker quantization dimension results for self-similar measures |
| topic | Dynamical Systems Probability Primary 28A80, Secondary 28A78 |
| url | https://arxiv.org/abs/2601.20531 |